What is the answer to log_{x}(x+12)=2 ?

The answer to log_{x}(x+12)=2 is x=4

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log_{x}(x+12)=2

lo g_{x} (x + 12) = 2

x = 4

Solution steps

lo g_{x} (x + 12) = 2

Apply log rules

\frac{ln ( x + 12 )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( x + 12 )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (x + 12) = 2 ln (x)

Apply log rules

x + 12 = x^{2}

Solve

x + 12 = x^{2} : x = 4, x = - 3

x = 4, x = - 3

Verify Solutions:

x = 4

True

, x = - 3

False

The solution is

x = 4

lo g_{x + 1} (5 x + 19) = 2

lo g_{13} (- x) + 5 = 8

ln (x) = 6.188235491

lo g_{3} (5 x - 1) = lo g_{3} (x + 7)

lo g_{8} (3) + lo g_{8} (- 4 x) = 1