Question

Solve the equation 2^3x+1=5^-x and round your answer to two digits after the decimal sign.

Answer 1

add log on both sides

Answer 2

(3x+1)log2 = -xlog5
3xlog2 +log2 = -xlog5
3xlog2 + xlog5 = -log2
x(3log2+log5) = -log2
x = -log2/(3log2+log5)

Answer 3

use the idea that
\[ \log(a^b) = b\ \log(a) \]
you can use any log, but log base 10 or natural log ln are available on a calculator