What is the answer to log_{x+5}(8)=log_{6}(8) ?

The answer to log_{x+5}(8)=log_{6}(8) is x=8^{1/(3log_{6)(2)}}-5

Solve for x: log_{x+5}(8)=log_{6}(8)

The solution is x=8^{1/(3log_{6)(2)}}-5

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lo g_{x + 5} (8) = lo g_{6} (8)

x = 8^{\frac{1}{3 l o g _{6} ( 2 )}} - 5

Decimal Notation

x = 1

Solution steps

lo g_{x + 5} (8) = lo g_{6} (8)

Apply log rules

\frac{1}{lo g _{8} ( x + 5 )} = 3 lo g_{6} (2)

Multiply both sides by

lo g_{8} (x + 5)

\frac{1}{lo g _{8} ( x + 5 )} lo g_{8} (x + 5) = 3 lo g_{6} (2) lo g_{8} (x + 5)

Simplify

1 = 3 lo g_{6} (2) lo g_{8} (x + 5)

Switch sides

3 lo g_{6} (2) lo g_{8} (x + 5) = 1

Divide both sides by

3 lo g_{6} (2)

lo g_{8} (x + 5) = \frac{1}{3 lo g _{6} ( 2 )}

Apply log rules

x + 5 = 8^{\frac{1}{3 l o g _{6} ( 2 )}}

Solve

x + 5 = 8^{\frac{1}{3 l o g _{6} ( 2 )}} : x = 8^{\frac{1}{3 l o g _{6} ( 2 )}} - 5

x = 8^{\frac{1}{3 l o g _{6} ( 2 )}} - 5

Verify Solutions:

x = 8^{\frac{1}{3 l o g _{6} ( 2 )}} - 5

True

The solution is

x = 8^{\frac{1}{3 l o g _{6} ( 2 )}} - 5

lo g_{3} (2 x + 9) - lo g_{3} (5 x) = 3

2 lo g_{2} (x) + 5 = 21

lo g_{5} (x + 7) + lo g_{5} (x - 4) = 3

∣ ln (x + 3) ∣ = 1

lo g_{3} (4) + lo g_{3} (x) = 1

What is the answer to log_{x+5}(8)=log_{6}(8) ?
The answer to log_{x+5}(8)=log_{6}(8) is x=8^{1/(3log_{6)(2)}}-5
Solve for x: log_{x+5}(8)=log_{6}(8)
The solution is x=8^{1/(3log_{6)(2)}}-5