What is the answer to log_{10}(5x)-log_{10}(x-1)=2 ?

The answer to log_{10}(5x)-log_{10}(x-1)=2 is x= 20/19

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

log_{10}(5x)-log_{10}(x-1)=2

lo g_{10} (5 x) - lo g_{10} (x - 1) = 2

x = \frac{20}{19}

Decimal Notation

x = 1.05263 \dots

Solution steps

lo g_{10} (5 x) - lo g_{10} (x - 1) = 2

Add

lo g_{10} (x - 1)

to both sides

lo g_{10} (5 x) - lo g_{10} (x - 1) + lo g_{10} (x - 1) = 2 + lo g_{10} (x - 1)

Simplify

lo g_{10} (5 x) = 2 + lo g_{10} (x - 1)

Apply log rules

5 x = 100 (x - 1)

Solve

5 x = 100 (x - 1) : x = \frac{20}{19}

x = \frac{20}{19}

Verify Solutions:

x = \frac{20}{19}

True

The solution is

x = \frac{20}{19}

3 lo g_{8} (2) = lo g_{8} (x)

112 = 238.36 ln (x) - 1690.9

lo g_{2} (5 x) + 4 lo g_{2} (3) = 5

lo g_{10} (\frac{x}{0.5}) = 0.25

lo g_{3} (z) = 3

What is the answer to log_{10}(5x)-log_{10}(x-1)=2 ?
The answer to log_{10}(5x)-log_{10}(x-1)=2 is x= 20/19
Solve for x: log_{10}(5x)-log_{10}(x-1)=2
The solution is x= 20/19