exponential exquations/log equation

Question

Solve the given equation for x.

(1/7)^x=2

 

I changed this to the log form

 

log(1/7)2=x

 

and then got the answer −1.69019608

 

this however is the wrong answer, the answer that I should come up with is -0.356207187108022.

 

I am not sure what i'm doing wrong with my exponential properties to get a number so much larger than what is right.

Answer 1

(1/7)^x = 2

x ln (1/7) = ln 2

x (ln 1 - ln 7) = ln 2

x = ln 2 / (ln1 - ln 7)

 

Can you calculate?