Answer:
[tex]x=2[/tex]
Step-by-step explanation:
So we have the equation:
[tex]5^x+5^{x+1}=150[/tex]
First, separate the second term:
[tex]5^x+(5\cdot5^x)=150[/tex]
Let u equal 5ˣ. So:
[tex]u+5u=150[/tex]
Combine like terms:
[tex]6u=150[/tex]
Divide both sides by 6:
[tex]u=25[/tex]
Substitute back u:
[tex]5^x=25[/tex]
Take the base 5 logarithm of both sides:
[tex]\log_5(5^x)=\log_5(25)[/tex]
The left cancels:
[tex]x=\log_5(25)[/tex]
Evaluate the right:
[tex]x=2[/tex]
So, our answer is 2.
And we're done!
