Solve the given equation for x

Question

8^x=4 

 

and 

 

9^-2x= (27) ^x-1

 

Answer 1

8^x=4

8=2^3

4=2^2

(2^3)^(x)=(2)^(2)

(2)^(3x)=2^(2)

if the bases are equal then the exponents must be equal

3x=2

x=2/3 answer

 

(9)^(-2x)=(27)^(x-1)

(3^2)^(-2x)=(3^3)^(x-1)

(3)^(-4x)=(3)^(3x-3)

equal bases mean equal exponents

-4x=3x-3

-4x-3x=-3

-7x=-3

7x=3

x=3/7 answer

Answer 2

First, recognize the powers.  8 = 2^3, 4 = 2^2. 

 

therefore, 8^x = 4 -->  (2^3)^x = 2^2  --> 2^3x = 2^2 --> 3x = 2 --> x = 2/3

 

9 = 3^2, 27 = 3^3

 

9^-2x = (27)^x-1 --> (3^2)^-2x = (3^3)^x-1 --> 3^-4x = 3^(3x-3) --> -4x = 3x-3 --> -7x = -3 --> x = 3/7