algebra 2 problem

Question

I need to solve the following exponential equation 9.3^x=(0.2)^-x with the exact answer and decimal places

Answer 1

 The only way the two can be equal is if x = 0.

 

9.3⁰ = (0.2)⁰

1 = 1

Answer 2

9.3^x = (0.2)^-x

 

9.3^x 0.2^x = 1

 

1.86^x = 1

 

log_1.86 1.86^x = log_1.86 1

 

x = log_1.86 1 = 0

 

Note that log_b 1 = 0 for any base b since b⁰ = 1 by definition.