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

The answer to log_{x-3}(2x)=3 is x\approx 5.17998…

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

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

x \approx 5.17998 \dots

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (x - 3)

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

Simplify

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

Apply log rules

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

Solve

2 x = (x - 3)^{3} : x \approx 5.17998 \dots

x \approx 5.17998 \dots

Verify Solutions:

x \approx 5.17998 \dots

True

The solution is

x \approx 5.17998 \dots

lo g_{6} (x + 9) - lo g_{36} (x) = 1

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

3 ln (5 x) = 15

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

x, 2 ln (x) + 1 = 0

What is the answer to log_{x-3}(2x)=3 ?
The answer to log_{x-3}(2x)=3 is x\approx 5.17998…
Solve for x: log_{x-3}(2x)=3
The solution is x\approx 5.17998…