What is the answer to (ln(3x-1))/(ln(x-1))=3 ?

The answer to (ln(3x-1))/(ln(x-1))=3 is x=3

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(ln(3x-1))/(ln(x-1))=3

\frac{ln ( 3 x - 1 )}{ln ( x - 1 )} = 3

x = 3

Solution steps

\frac{ln ( 3 x - 1 )}{ln ( x - 1 )} = 3

Multiply both sides by

ln (x - 1)

\frac{ln ( 3 x - 1 )}{ln ( x - 1 )} ln (x - 1) = 3 ln (x - 1)

Simplify

ln (3 x - 1) = 3 ln (x - 1)

Apply log rules

3 x - 1 = (x - 1)^{3}

Solve

3 x - 1 = (x - 1)^{3} : x = 0, x = 3

x = 0, x = 3

Verify Solutions:

x = 0

False

, x = 3

True

The solution is

x = 3

lo g_{10} (x) + lo g_{10} (x + 48) = 2

lo g_{10} (x) - lo g_{10} (x - 3) = 2

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

x, y = 4 \cdot ln (x + c)

2 = 2 x + ln (x)

What is the answer to (ln(3x-1))/(ln(x-1))=3 ?
The answer to (ln(3x-1))/(ln(x-1))=3 is x=3
Solve for x: (ln(3x-1))/(ln(x-1))=3
The solution is x=3