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

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

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

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

x = 3

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (x)

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

Simplify

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

Apply log rules

4 x - 3 = x^{2}

Solve

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

x = 3, x = 1

Verify Solutions:

x = 3

True

, x = 1

False

The solution is

x = 3

0.32 = lo g_{10} (x)

4 lo g_{3} (x - 40) = 16

lo g_{2} (5 x - 8) = 1

lo g_{10} (x) + lo g_{10} (x) = 2

lo g_{3} (x - 2) + lo g_{3} (2 x - 7) = 2