log4(x+2)=3

After you get the answer, try looking at different rules. This stuff will catch you by suprise, as some college teachers like to bring in out of to test.

log4(x+2)=3

A)

\(log(4(x+2))=3\\10^3=4(x+2)\\4x+8=1000\\x=\frac{1000-8}{4}\\\color{blue}x=248\)

B)

\(log(4 )\cdot (x+2)=3\\log\ 4=\frac{3}{x+2}\\x+2=\frac{3}{log\ 4}\\x=\frac{3}{log\ 4}-2\\\color{blue}x=2.98289214233\)

C)

\(log_4(x+2)=3\\4^3=x+2\\x=4^3-2\\\color{blue}x=62\)

  !        Look for a solution.

Solve for x:
(log(x + 2))/(log(4)) = 3

Multiply both sides by log(4):
log(x + 2) = 3 log(4)

3 log(4) = log(4^3) = log(64):
log(x + 2) = log(64)

Cancel logarithms by taking exp of both sides:
x + 2 = 64

Subtract 2 from both sides:
Answer: | x = 62