Question

5^x + 5^x+1= 150
Find x
Help me pls i need soon
Tksss

Answer 1

`x=2`

Explanation:

So we have the equation:

`5^x+5^(x+1)=150`

First, separate the second term:

`5^x+(5\cdot5^x)=150`

Let u equal 5ˣ. So:

`u+5u=150`

Combine like terms:

`6u=150`

Divide both sides by 6:

`u=25`

Substitute back u:

`5^x=25`

Take the base 5 logarithm of both sides:

`\log_5(5^x)=\log_5(25)`

The left cancels:

`x=\log_5(25)`

Evaluate the right:

`x=2`

So, our answer is 2.

And we're done!