What is the answer to log_{x-2}(81)=4 ?

The answer to log_{x-2}(81)=4 is x=5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

log_{x-2}(81)=4

lo g_{x - 2} (81) = 4

x = 5

Solution steps

lo g_{x - 2} (81) = 4

Apply log rules

\frac{1}{lo g _{81} ( x - 2 )} = 4

Multiply both sides by

lo g_{81} (x - 2)

\frac{1}{lo g _{81} ( x - 2 )} lo g_{81} (x - 2) = 4 lo g_{81} (x - 2)

Simplify

1 = 4 lo g_{81} (x - 2)

Switch sides

4 lo g_{81} (x - 2) = 1

Divide both sides by

4

lo g_{81} (x - 2) = \frac{1}{4}

Apply log rules

x - 2 = 3

Solve

x - 2 = 3 : x = 5

x = 5

Verify Solutions:

x = 5

True

The solution is

x = 5

lo g_{5} (x) + 6 lo g_{x} (5) = 5

ln (3 x + 1) - ln (x) = - 2

5 lo g_{7} (n) = 10

lo g_{4} (4 x) + 2 lo g_{4} (4) = 0

- lo g_{10} (x) = 11.45