What is the answer to log_{x}(2x+24)=2 ?

The answer to log_{x}(2x+24)=2 is x=6

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log_{x}(2x+24)=2

lo g_{x} (2 x + 24) = 2

x = 6

Solution steps

lo g_{x} (2 x + 24) = 2

Apply log rules

\frac{ln ( 2 x + 24 )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( 2 x + 24 )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (2 x + 24) = 2 ln (x)

Apply log rules

2 x + 24 = x^{2}

Solve

2 x + 24 = x^{2} : x = 6, x = - 4

x = 6, x = - 4

Verify Solutions:

x = 6

True

, x = - 4

False

The solution is

x = 6

lo g_{2} (2 x + 5) = 4

lo g_{6} (x) = - 4

2 ln (x) + 1 = ln (2 x)

lo g_{3} (x + 2) = 0

lo g_{x} (0.4) = - 2