What is the answer to log_{3x+2}(8)=log_{5}(2) ?

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

Solve for x: log_{3x+2}(8)=log_{5}(2)

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

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

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

Solution steps

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

Apply log rules

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

Multiply both sides by

lo g_{8} (3 x + 2)

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

Simplify

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

Switch sides

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

Divide both sides by

lo g_{5} (2)

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

Apply log rules

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

Solve

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

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

Verify Solutions:

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

True

The solution is

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

lo g_{b} (3) = 10

lo g_{2} (x - 1) + lo g_{2} (2 x - 1) = 0

7.3 = lo g_{10} (x)

lo g_{6} (8 - 3 x) = 1

\frac{9}{2} lo g_{4} (x) = 7

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