Question

(3/4)^x=(16/9)

Answer 1

Use log to find the x :
Suppose : \[a ^{x} = b\]
\[\log_{a} b = x\]

Now following that we get,

\[\log_{3/4} 16/9 = x\]
Put that in your calculator and you will get x = -2 answer :)

Answer 2

\(\bf \left(\cfrac{3}{4}\right)^x=\cfrac{16}{9}\implies \cfrac{3^x}{4^x}=\cfrac{16}{9}\qquad recall\implies {\color{blue}{ 16\implies 4^2\qquad 9\implies 3^2}}\)

Answer 3

but the answer is -2 not 2 jdoe

Answer 4

In this one we are actually supposed to solve without using logs.

Answer 5

but you are correct the answer is -2 not 2, I'm not sure I understand why though, is it because we are working with fractions?

Answer 6

well... ahemm I didn't say it was 2, I just pointed out the values

Answer 7

so is it negative because of the fraction?