MATH SOLVE

3 months ago

Q:
# What is the solution of the equation 4^(x + 1) = 21? Round your answer to the nearest ten-thousandth.

Accepted Solution

A:

For this case we must solve the following equation:[tex]4 ^ {x + 1} = 21[/tex]We find Neperian logarithm on both sides:[tex]ln (4 ^ {x + 1}) = ln (21)[/tex]According to the rules of Neperian logarithm we have:[tex](x + 1) ln (4) = ln (21)[/tex]We apply distributive property:[tex]xln (4) + ln (4) = ln (21)[/tex]We subtract ln (4) on both sides:[tex]xln (4) = ln (21) -ln (4)[/tex]We divide between ln (4) on both sides:[tex]x = \frac {ln (21)} {ln (4)} - \frac {ln (4)} {ln (4)}\\x = \frac {ln (21)} {ln (4)} - 1\\x = 1,19615871[/tex]Rounding:[tex]x = 1.1962[/tex]Answer:x = 1.1962