What is the answer to 5log_{3}(y)=9+log_{y}(9) ?

The answer to 5log_{3}(y)=9+log_{y}(9) is y=9,y= 1/(\sqrt[5]{3)}

Solve for y: 5log_{3}(y)=9+log_{y}(9)

The solution is y=9,y= 1/(\sqrt[5]{3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

5 lo g_{3} (y) = 9 + lo g_{y} (9)

Decimal Notation

y = 9, y = 0.80274 \dots

Solution steps

5 lo g_{3} (y) = 9 + lo g_{y} (9)

Apply log rules

5 lo g_{3} (y) = 9 + \frac{2}{lo g _{3} ( y )}

Rewrite the equation with

lo g_{3} (y) = u

5 u = 9 + \frac{2}{u}

Solve

5 u = 9 + \frac{2}{u} : u = 2, u = - \frac{1}{5}

u = 2, u = - \frac{1}{5}

Substitute back

u = lo g_{3} (y),

solve for

y

Solve

lo g_{3} (y) = 2 : y = 9

Solve

Verify Solutions:

y = 9

True

The solutions are

a, lo g_{5} (a) = 12

lo g_{x} (10) = \frac{1}{4}

lo g_{x} (100000) = 3

0.4634 = 0.6446 ln (x) - 0.5557

lo g_{10} (343) = 3 lo g_{10} (x)

What is the answer to 5log_{3}(y)=9+log_{y}(9) ?
The answer to 5log_{3}(y)=9+log_{y}(9) is y=9,y= 1/(\sqrt[5]{3)}
Solve for y: 5log_{3}(y)=9+log_{y}(9)
The solution is y=9,y= 1/(\sqrt[5]{3)}