What is the answer to log_{x}(3x+4)=2 ?

The answer to log_{x}(3x+4)=2 is x=4

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log_{x}(3x+4)=2

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

x = 4

Solution steps

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

Apply log rules

\frac{ln ( 3 x + 4 )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( 3 x + 4 )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (3 x + 4) = 2 ln (x)

Apply log rules

3 x + 4 = x^{2}

Solve

3 x + 4 = x^{2} : x = 4, x = - 1

x = 4, x = - 1

Verify Solutions:

x = 4

True

, x = - 1

False

The solution is

x = 4

2 ln (3 x - 3) = 3

2 lo g_{2} (x) - 3 lo g_{x} (2) + 5 = 0

e^{2 l n (x)} = x^{2}

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

0.2 = - lo g_{10} (x)