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

The answer to log_{x-4}(3x)=3 is x\approx 6.72189…

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

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

x \approx 6.72189 \dots

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (x - 4)

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

Simplify

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

Apply log rules

3 x = (x - 4)^{3}

Solve

3 x = (x - 4)^{3} : x \approx 6.72189 \dots

x \approx 6.72189 \dots

Verify Solutions:

x \approx 6.72189 \dots

True

The solution is

x \approx 6.72189 \dots

ln (\frac{x}{10}) = 4

x = e^{l n (x)}

5 + 2 ln (x) = 1

9 lo g_{9} (3 x - 5) = x + 7

3 lo g_{10} (x) = lo g_{10} (64)

What is the answer to log_{x-4}(3x)=3 ?
The answer to log_{x-4}(3x)=3 is x\approx 6.72189…
Solve for x: log_{x-4}(3x)=3
The solution is x\approx 6.72189…