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

The answer to log_{5}(x+1)-log_{5}(x-1)=1 is x= 3/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

log_{5}(x+1)-log_{5}(x-1)=1

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

x = \frac{3}{2}

Decimal Notation

x = 1.5

Solution steps

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

Add

lo g_{5} (x - 1)

to both sides

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

Simplify

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

Apply log rules

x + 1 = 5 (x - 1)

Solve

x + 1 = 5 (x - 1) : x = \frac{3}{2}

x = \frac{3}{2}

Verify Solutions:

x = \frac{3}{2}

True

The solution is

x = \frac{3}{2}

lo g_{2} (4 x) - 4 lo g_{2} (2) = 0

lo g_{10} (x) (32) = 5

ln (ln (ln (x))) = 0

ln (x) + ln (8 x) = - 2

150 = 21392 ln (x) - 65652

What is the answer to log_{5}(x+1)-log_{5}(x-1)=1 ?
The answer to log_{5}(x+1)-log_{5}(x-1)=1 is x= 3/2
Solve for x: log_{5}(x+1)-log_{5}(x-1)=1
The solution is x= 3/2