What is the answer to solvefor x,log_{x}(6x+16)=2 ?

The answer to solvefor x,log_{x}(6x+16)=2 is x=8

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solvefor x,log_{x}(6x+16)=2

solve for

x, lo g_{x} (6 x + 16) = 2

x = 8

Solution steps

lo g_{x} (6 x + 16) = 2

Apply log rules

\frac{ln ( 6 x + 16 )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( 6 x + 16 )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (6 x + 16) = 2 ln (x)

Apply log rules

6 x + 16 = x^{2}

Solve

6 x + 16 = x^{2} : x = 8, x = - 2

x = 8, x = - 2

Verify Solutions:

x = 8

True

, x = - 2

False

The solution is

x = 8

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

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

ln (x) - ln (2) = 0

2^{4} = 16 lo g_{2} (x)

lo g_{2} (4 x - 12) = 5

What is the answer to solvefor x,log_{x}(6x+16)=2 ?
The answer to solvefor x,log_{x}(6x+16)=2 is x=8