What is the answer to log_{x-8}(x^2-16)=2 ?

The answer to log_{x-8}(x^2-16)=2 is No Solution for x\in\mathbb{R}

Solve for x: log_{x-8}(x^2-16)=2

The solution is No Solution for x\in\mathbb{R}

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lo g_{x - 8} (x^{2} - 16) = 2

No Solution for x \in R

Solution steps

lo g_{x - 8} (x^{2} - 16) = 2

Apply log rules

\frac{ln ( x ^{2} - 16 )}{ln ( x - 8 )} = 2

Multiply both sides by

ln (x - 8)

\frac{ln ( x ^{2} - 16 )}{ln ( x - 8 )} ln (x - 8) = 2 ln (x - 8)

Simplify

ln (x^{2} - 16) = 2 ln (x - 8)

Apply log rules

x^{2} - 16 = (x - 8)^{2}

Solve

x^{2} - 16 = (x - 8)^{2} : x = 5

x = 5

Verify Solutions:

x = 5

False

The solution is

No Solution for x \in R

lo g_{1} (x) = 1.755

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

y, x = 10 lo g_{2} (y)

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

lo g_{x} (x) = 2

What is the answer to log_{x-8}(x^2-16)=2 ?
The answer to log_{x-8}(x^2-16)=2 is No Solution for x\in\mathbb{R}
Solve for x: log_{x-8}(x^2-16)=2
The solution is No Solution for x\in\mathbb{R}