What is the answer to log_{x}(2x+15)=2 ?

The answer to log_{x}(2x+15)=2 is x=5

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log_{x}(2x+15)=2

lo g_{x} (2 x + 15) = 2

x = 5

Solution steps

lo g_{x} (2 x + 15) = 2

Apply log rules

\frac{ln ( 2 x + 15 )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( 2 x + 15 )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (2 x + 15) = 2 ln (x)

Apply log rules

2 x + 15 = x^{2}

Solve

2 x + 15 = x^{2} : x = 5, x = - 3

x = 5, x = - 3

Verify Solutions:

x = 5

True

, x = - 3

False

The solution is

x = 5

ln (x) = 3.967503513

lo g_{10} (5 x) - lo g_{10} (x - 1) = 2

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

112 = 238.36 ln (x) - 1690.9

lo g_{2} (5 x) + 4 lo g_{2} (3) = 5