What is the answer to log_{3}(x^{log_{3}(x)})=4 ?

The answer to log_{3}(x^{log_{3}(x)})=4 is x=9,x= 1/9

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

log_{3}(x^{log_{3}(x)})=4

lo g_{3} (x^{l o g_{3} (x)}) = 4

x = 9, x = \frac{1}{9}

Decimal Notation

x = 9, x = 0.11111 \dots

Solution steps

lo g_{3} (x^{l o g_{3} (x)}) = 4

Apply exponent rules

lo g_{3} (e^{l o g_{3} (x) l n (x)}) = 4

Rewrite the equation with

e^{l o g_{3} (x) l n (x)} = u

lo g_{3} (u) = 4

Solve

lo g_{3} (u) = 4 : u = 81

u = 81

Substitute back

u = e^{l o g_{3} (x) l n (x)},

solve for

x

Solve

e^{l o g_{3} (x) l n (x)} = 81 : x = 9, x = \frac{1}{9}

x = 9, x = \frac{1}{9}

Verify Solutions:

x = 9

True

, x = \frac{1}{9}

True

The solutions are

x = 9, x = \frac{1}{9}

1050 = 480 e^{7 r}

5^{x} + 5^{x + 1} - \frac{6}{25} = 0

2^{x + 1} + 2^{x} + 2^{x - 1} = 14

7^{x} = 4

6 (6^{2 x}) - 37 (6^{x}) + 6 = 0

What is the answer to log_{3}(x^{log_{3}(x)})=4 ?
The answer to log_{3}(x^{log_{3}(x)})=4 is x=9,x= 1/9
Solve for x: log_{3}(x^{log_{3}(x)})=4
The solution is x=9,x= 1/9