What is the answer to log_{5}(x/(x-8))=3 ?

The answer to log_{5}(x/(x-8))=3 is x= 250/31

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log_{5}(x/(x-8))=3

lo g_{5} (\frac{x}{x - 8}) = 3

x = \frac{250}{31}

Decimal

x = 8.06451 \dots

Solution steps

lo g_{5} (\frac{x}{x - 8}) = 3

Apply log rules

\frac{x}{x - 8} = 5^{3}

Multiply both sides by

x - 8

\frac{x}{x - 8} (x - 8) = 5^{3} (x - 8)

Simplify

x = 125 (x - 8)

Solve

x = 125 (x - 8) : x = \frac{250}{31}

x = \frac{250}{31}

Verify Solutions:

x = \frac{250}{31}

True

The solution is

x = \frac{250}{31}

lo g_{4 x} (5) = 3

ln (x) + ln (\frac{1}{x} + 1) = 3

x, ln (ln (x)) = 0

lo g_{x} (336) = 2

lo g_{7} (3 - x) = 2 lo g_{7} (4)

What is the answer to log_{5}(x/(x-8))=3 ?
The answer to log_{5}(x/(x-8))=3 is x= 250/31
Solve for x: log_{5}(x/(x-8))=3
The solution is x= 250/31