What is the answer to log_{10}(x)-2log_{x}(10)=1 ?

The answer to log_{10}(x)-2log_{x}(10)=1 is x=100,x= 1/10

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

log_{10}(x)-2log_{x}(10)=1

lo g_{10} (x) - 2 lo g_{x} (10) = 1

x = 100, x = \frac{1}{10}

Decimal Notation

x = 100, x = 0.1

Solution steps

lo g_{10} (x) - 2 lo g_{x} (10) = 1

Apply log rules

lo g_{10} (x) - \frac{2}{lo g _{10} ( x )} = 1

Rewrite the equation with

lo g_{10} (x) = u

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

Solve

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

u = 2, u = - 1

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

lo g_{10} (x) = 2 : x = 100

Solve

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

x = 100, x = \frac{1}{10}

Verify Solutions:

x = 100

True

, x = \frac{1}{10}

True

The solutions are

x = 100, x = \frac{1}{10}

ln (x) - ln (x - 2000) = 14876

lo g_{2} (2 x + 1) - lo g_{2} (x + 2) = 3

2 lo g_{3} (x) = lo g_{3} (16)

lo g_{x} (3) = \frac{3}{2}

x, lo g_{10} (x) = ln (y)

What is the answer to log_{10}(x)-2log_{x}(10)=1 ?
The answer to log_{10}(x)-2log_{x}(10)=1 is x=100,x= 1/10
Solve for x: log_{10}(x)-2log_{x}(10)=1
The solution is x=100,x= 1/10