Question

Please help ASAP! Than you very much! Just want confirm my answer it is -8 or -4. Solve 6Bx-2%7D" id="TexFormula1" title="^{x-2}" alt="^{x-2}" align="absmiddle" class="latex-formula"> =36 $^{x+3}$. Or 6^(x-2) = 36 ^(x+3).

Answer 1

Answer:  x = -8

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Work Shown:

6^(x-2) = 36^(x+3)

6^(x-2) = ( 6^2 )^(x+3) ... replace 36 with 6^2

6^(x-2) = 6^(2(x+3)) .... use the rule (a^b)^c = a^(b*c)

6^(x-2) = 6^(2x+6) .... distribute

x-2 = 2x+6 .... bases are both 6, so the exponents must be equal

2x+6 = x-2

2x-x = -2-6

x = -8 This is the only solution

Alternatively, you can use logarithms to solve for x. Though in my opinion that is a messier route to take.

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Checking the answer:

Plug x = -8 into the original equation. Simplify both sides. We should get the same value on both sides. If not, then we made an error in solving for x

6^(x-2) = 36^(x+3)

6^(-8-2) = 36^(-8+3)

6^(-10) = 36^(-5)

0.00000001653818 = 0.00000001653818

We get the same value on both sides. This confirms we have the right answer.