What is the answer to log_{x}(2x+80)=2 ?

The answer to log_{x}(2x+80)=2 is x=10

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log_{x}(2x+80)=2

lo g_{x} (2 x + 80) = 2

x = 10

Solution steps

lo g_{x} (2 x + 80) = 2

Apply log rules

\frac{ln ( 2 x + 80 )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( 2 x + 80 )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (2 x + 80) = 2 ln (x)

Apply log rules

2 x + 80 = x^{2}

Solve

2 x + 80 = x^{2} : x = 10, x = - 8

x = 10, x = - 8

Verify Solutions:

x = 10

True

, x = - 8

False

The solution is

x = 10

lo g_{x} (3) = 0

lo g_{x} (3) = 7

- 3 lo g_{7} (3) = lo g_{7} (z)

lo g_{x} (3) = 2

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