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

The answer to log_{x}(2x+8)=2 is x=4

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log_{x}(2x+8)=2

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

x = 4

Solution steps

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

Apply log rules

\frac{ln ( 2 x + 8 )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( 2 x + 8 )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (2 x + 8) = 2 ln (x)

Apply log rules

2 x + 8 = x^{2}

Solve

2 x + 8 = x^{2} : x = 4, x = - 2

x = 4, x = - 2

Verify Solutions:

x = 4

True

, x = - 2

False

The solution is

x = 4

lo g_{2} (5 - y) = 1

lo g_{25} (x) = - \frac{1}{2}

ln (5) + ln (y^{2} - 1) - ln (y - 1) = 2

ln (x^{2} + 1) = 1 + 2 ln (x)

ln (x) + ln (x - 8) = 4