What is the answer to log_{a}(a^n)=n ?

The answer to log_{a}(a^n)=n is No Solution for a\in\mathbb{R}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

log_{a}(a^n)=n

lo g_{a} (a^{n}) = n

No Solution for a \in R

Solution steps

lo g_{a} (a^{n}) = n

Apply log rules

\frac{ln ( a ^{n} )}{ln ( a )} = n

Multiply both sides by

ln (a)

\frac{ln ( a ^{n} )}{ln ( a )} ln (a) = n ln (a)

Simplify

ln (a^{n}) = n ln (a)

Apply log rules

n ln (a) = n ln (a)

Rewrite the equation with

ln (a) = u

n u = n u

Both sides are equal

True for all u

Verify Solutions:

a < 0

False

, a = 0

False

, a > 0

False

The solution is

No Solution for a \in R

lo g_{3} (x) = 3 - 2 lo g_{x} (3)

- 0.15 = lo g_{10} (x)

lo g_{2} (x) = 8

5 = 10 lo g_{10} (x)

4 lo g_{3} (x) = lo g_{9} (x) + 2

What is the answer to log_{a}(a^n)=n ?
The answer to log_{a}(a^n)=n is No Solution for a\in\mathbb{R}