Styling Navigation bar with logo and button

Question

I have been trying for hours to style my navigation bar(which is horizontal at the top of the screen) so that my logo will show at left , menu on the center and the username with the logout button at right(all of them horizontally).I tried float ,position display, but nothing seems to work as i want.Instead the result is all the elements(logo,menu,username,logout button) to appear in the center.Any help would be appreciated.

HTML code

 <header>   
     <div class="page">
   <nav class="page__menu page__custom-settings menu">
    <div class="logo">
   <img src="images/logo.png">
    </div>
    <ul class="menu__list r-list">
      <li class="menu__group"><a href="index.php" class="menu__link r-link text-underlined">Main</a></li>
      <li class="menu__group"><a href="main.php" class="menu__link r-link text-underlined">Songs</a></li>
      <li class="menu__group"><a href="ratings.php" class="menu__link r-link text-underlined">Ratings</a></li>
    </ul>   
    
     <section id="login">
                <a href="registration/logout.php" class="button">Logout</a>
                <h1>User: <?php   echo $user_data['user_name']; ?></h1>
                </section>  
  </nav>     
    </header>

CSS code

.r-link{
  display: var(--rLinkDisplay, inline-flex) !important;
}

.r-link[href]{
  color: var(--rLinkColor) !important;
  text-decoration: var(--rLinkTextDecoration, none) !important;
}

.r-list{
  padding-right: var(--rListPaddingRight, 0) !important;
  margin-top: var(--rListMarginTop, 0) !important;
  margin-bottom: var(--rListMarginBottom, 0) !important;
  margin-left: var(--rListMarginLeft, 0) !important;
  list-style: var(--rListListStyle, none) !important;
  
}

.menu{
  --rLinkColor: var(--menuLinkColor, currentColor);
   display: flex;
  justify-content: center;
  
}

.menu__link{
  display: var(--menuLinkDisplay, block);
 
}

.menu__link:focus{
  outline: var(--menuLinkOutlineWidth, 2px) solid var(--menuLinkOutlineColor, currentColor);
  outline-offset: var(--menuLinkOutlineOffset);
}

.menu__link:hover{
  --rLinkColor: #e8491d; ;
}

.menu{
  background-color: var(--menuBackgroundColor, #f0f0f0);
  box-shadow: var(--menuBoxShadow, 0 1px 3px 0 rgba(0, 0, 0, .12), 0 1px 2px 0 rgba(0, 0, 0, .24));
}

.menu__list{
  display : flex;
}

.page__menu img{
      float: left;
    position: relative;
    margin: 10px 15px 15px 10px;
    display: block;
     width: 450px;
      max-width:100% ;
      height: auto;
      margin: auto;
}

.menu__link{
  padding: var(--menuLinkPadding, 1.5rem 2.5rem);
  font-weight: 700;
  text-transform: uppercase;
}

.text-underlined{
  position: relative;
  overflow: hidden;
  will-change: color;
  transition: color .25s ease-out;  
}

.text-underlined::before, 
.text-underlined::after{
  content: "";
  width: 0;
  height: 3px;
  background-color: var(--textUnderlinedLineColor, currentColor);
  will-change: width;
  transition: width .1s ease-out;
  position: absolute;
  bottom: 0;
}

.text-underlined::before{
  left: 50%;
  transform: translateX(-50%); 
}

.text-underlined::after{
  right: 50%;
  transform: translateX(50%); 
}

.text-underlined:hover::before, 
.text-underlined:hover::after{
  width: 100%;
  transition-duration: .2s;
}

.page__custom-settings{
  --menuBackgroundColor: #255785;
  --menuLinkColor: #fff;
  --menuLinkColorUnactive: #241c69;
  --menuLinkOutlineOffset: -.5rem; 
}
.button {
  background-color: #e8491d; 
  color: white;
  padding: 10px 12px;
  text-align: center;
  text-decoration: none;
  display: inline-block;
  font-size: 16px;
  margin: 7px 7px;
  transition-duration: 0.4s;
  cursor: pointer;
  float : right;   
}
.button:hover {
  box-shadow: 0 12px 16px 0 rgba(0,0,0,0.24),0 17px 50px 0 rgba(0,0,0,0.19);
}
h1 {
  text-align: right;
  font-size: 14px;
  font-weight: bold;
  font-family: "Times New Roman", Times, serif;
  color: white;
  padding: 20px;
}

Answer 1

Here is the result what I fixed, please check and let me know. You need to change justify-content: space-between instead center to the menu and add align-items: center and align-items: center to the #login. Added the fixed css code. Hope it is helpful~

.r-link {
    display: var(--rLinkDisplay, inline-flex) !important;
}

.r-link[href] {
    color: var(--rLinkColor) !important;
    text-decoration: var(--rLinkTextDecoration, none) !important;
}

.r-list {
    padding-right: var(--rListPaddingRight, 0) !important;
    margin-top: var(--rListMarginTop, 0) !important;
    margin-bottom: var(--rListMarginBottom, 0) !important;
    margin-left: var(--rListMarginLeft, 0) !important;
    list-style: var(--rListListStyle, none) !important;

}

.menu {
    --rLinkColor: var(--menuLinkColor, currentColor);
    display: flex;
    justify-content: space-between;
    align-items: center;

}

.menu__link {
    display: var(--menuLinkDisplay, block);

}

.menu__link:focus {
    outline: var(--menuLinkOutlineWidth, 2px) solid var(--menuLinkOutlineColor, currentColor);
    outline-offset: var(--menuLinkOutlineOffset);
}

.menu__link:hover {
    --rLinkColor: #e8491d;
}

.menu {
    background-color: var(--menuBackgroundColor, #f0f0f0);
    box-shadow: var(--menuBoxShadow, 0 1px 3px 0 rgba(0, 0, 0, .12), 0 1px 2px 0 rgba(0, 0, 0, .24));
}

.menu__list {
    display: flex;
    padding-left: 0;
}

.page__menu img {
    float: left;
    position: relative;
    margin: 10px 15px 15px 10px;
    display: block;
    width: 450px;
    max-width: 100%;
    height: auto;
    margin: auto;
}

#login {
    display: flex;
    align-items: center;
}

.menu__link {
    padding: var(--menuLinkPadding, 1.5rem 2.5rem);
    font-weight: 700;
    text-transform: uppercase;
}

.text-underlined {
    position: relative;
    overflow: hidden;
    will-change: color;
    transition: color .25s ease-out;
}

.text-underlined::before,
.text-underlined::after {
    content: "";
    width: 0;
    height: 3px;
    background-color: var(--textUnderlinedLineColor, currentColor);
    will-change: width;
    transition: width .1s ease-out;
    position: absolute;
    bottom: 0;
}

.text-underlined::before {
    left: 50%;
    transform: translateX(-50%);
}

.text-underlined::after {
    right: 50%;
    transform: translateX(50%);
}

.text-underlined:hover::before,
.text-underlined:hover::after {
    width: 100%;
    transition-duration: .2s;
}

.page__custom-settings {
    --menuBackgroundColor: #255785;
    --menuLinkColor: #fff;
    --menuLinkColorUnactive: #241c69;
    --menuLinkOutlineOffset: -.5rem;
}

.button {
    background-color: #e8491d;
    color: white;
    padding: 10px 12px;
    text-align: center;
    text-decoration: none;
    display: inline-block;
    font-size: 16px;
    margin: 7px 7px;
    transition-duration: 0.4s;
    cursor: pointer;
    float: right;
}

.button:hover {
    box-shadow: 0 12px 16px 0 rgba(0, 0, 0, 0.24), 0 17px 50px 0 rgba(0, 0, 0, 0.19);
}

h1 {
    text-align: right;
    font-size: 14px;
    font-weight: bold;
    font-family: "Times New Roman", Times, serif;
    color: white;
    padding: 20px;
}