Question

(2/3)^x=3.375. Solve for x

Answer 1

I'll write log, you can use any base logs you like.

$(2/3)^x = 3.375=27/8$

$x \log(2/3) = \log(27/8)$

$x = \dfrac{\log(27/8)}{\log(2/3)}}$

$x = \dfrac{\log( (3/2)^3)}{\log(2/3)}}$

$x = \dfrac{\log( (2/3)^{-3})}{\log(2/3)}}$

$x = \dfrac{-3 \log(2/3)}{\log(2/3)}}$

$x = -3$

Answer: -3