Question

Solve 5^x/2 = 21

Answer 1

start with 5^x = 42

then

\[x = \log _{5} 42\]

if you don't have base 5 logs then use change of base

change to base e logs

\[x = \ln(42)/\ln(5) \]

x is approx 2.32222

to check use 5^(2.3222) do you get an answer close to 42..?

Answer 2

5^x = 2 * 21 = 42
-> x = log (5) 42 = 2.32

Answer 3

if the problem is

\[5^{x/2} = 21\]

same process

\[x/2 = \log _{5} (21)\]

do the change of base and solve for x