What is the solution to the equation g^(x-2)=27

First problem: Solving for g.

Second problem: Solving for x.

Third problem: Assuming g is 9 while solving for x.

Step-by-step explanation:

First problem: Solving for g.

Raise both sides by 1/(x-2).

Second problem: Solving for x.

x is in the exponent so we have to convert to logarithm form since we desire to solve for it:

Add 2 on both sides:

Third problem: Assuming g is 9 while solving for x.

I'm going to solve this in a different way than I did above but you could solve it exactly the way I did for x when 9 was g.

I'm going to write both 9 and 27 as 3 to some power.

9=3^2 while 27=3^3.

Since both bases are the same on both sides, we need the exponents to be the same:

Add 4 on both sides:

Divide both sides by 2:

Now earlier for x in terms of g we got:

I we input 9 in place of g and put it into our calculator or use some tricks without the calculator to compute we should get 3.5 as the answer like we did above when g was 9.

-2

7 - 9 = -2

reversed:

-2 + 9 = 7