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Find \(x\) if \(7^{4x + 10} = 7^{2x}.\)

 Apr 22, 2023
 #1
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+1

We can solve for x by equating the exponents in the equation 7^(4x + 10) = 7^(2x). This gives us 4x + 10 = 2x. Solving for x, we get x = 5/2.

Therefore, x = 5/2.

 Apr 22, 2023
 #2
avatar+90 
+1

You were close, guest, but when you solve for x, x=-5.

4x+10=2x

-2x.     -2x

2x+10=0

     -10 -10

2x=-10

/2.    /2

x=-10/2

x=-

But your first steps were correct, so kudos to that!

 Apr 22, 2023

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