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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

log_{x-2}(4)=2

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

x = 4

Solution steps

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

Apply log rules

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

Multiply both sides by

lo g_{4} (x - 2)

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

Simplify

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

Switch sides

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

Divide both sides by

2

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

Apply log rules

x - 2 = 2

Solve

x - 2 = 2 : x = 4

x = 4

Verify Solutions:

x = 4

True

The solution is

x = 4

ln (x) = 4.7732100000000 \dots

lo g_{10} (x) = 243

lo g_{a} (2) + 2 lo g_{a} (7) = 2

0.5 = - lo g_{10} (t)

ln (x + 4) + ln (x + 5) = 1