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

The answer to log_{x-4}(x)=3 is x\approx 5.79632…

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log_{x-4}(x)=3

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

x \approx 5.79632 \dots

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (x - 4)

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

Simplify

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

Apply log rules

x = (x - 4)^{3}

Solve

x = (x - 4)^{3} : x \approx 5.79632 \dots

x \approx 5.79632 \dots

Verify Solutions:

x \approx 5.79632 \dots

True

The solution is

x \approx 5.79632 \dots

ln (x) = - ln (x)

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

lo g_{27} (a^{2}) = 18

lo g_{3} (4 - 3^{x - 1} - 1) = 2 x - 1

lo g_{3} (x) = 10

What is the answer to log_{x-4}(x)=3 ?
The answer to log_{x-4}(x)=3 is x\approx 5.79632…
Solve for x: log_{x-4}(x)=3
The solution is x\approx 5.79632…