What is the answer to log_{8}(x+5)-log_{8}(x-1)=1 ?

The answer to log_{8}(x+5)-log_{8}(x-1)=1 is x= 13/7

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log_{8}(x+5)-log_{8}(x-1)=1

lo g_{8} (x + 5) - lo g_{8} (x - 1) = 1

x = \frac{13}{7}

Decimal Notation

x = 1.85714 \dots

Solution steps

lo g_{8} (x + 5) - lo g_{8} (x - 1) = 1

Add

lo g_{8} (x - 1)

to both sides

lo g_{8} (x + 5) - lo g_{8} (x - 1) + lo g_{8} (x - 1) = 1 + lo g_{8} (x - 1)

Simplify

lo g_{8} (x + 5) = 1 + lo g_{8} (x - 1)

Apply log rules

x + 5 = 8 (x - 1)

Solve

x + 5 = 8 (x - 1) : x = \frac{13}{7}

x = \frac{13}{7}

Verify Solutions:

x = \frac{13}{7}

True

The solution is

x = \frac{13}{7}

ln (5 x - 4) = 3

ln (x) - ln (x + 1) = 0

y, ln (y + 3) = x

ln (x) = 11.478

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

What is the answer to log_{8}(x+5)-log_{8}(x-1)=1 ?
The answer to log_{8}(x+5)-log_{8}(x-1)=1 is x= 13/7
Solve for x: log_{8}(x+5)-log_{8}(x-1)=1
The solution is x= 13/7