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

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

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log_{x}(x+2)=2

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

x = 2

Solution steps

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

Apply log rules

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

Multiply both sides by

ln (x)

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

Simplify

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

Apply log rules

x + 2 = x^{2}

Solve

x + 2 = x^{2} : x = 2, x = - 1

x = 2, x = - 1

Verify Solutions:

x = 2

True

, x = - 1

False

The solution is

x = 2

lo g_{5} (y) = 40

0.58 = ln (x)

a, ln (a) = ln (b)

2 lo g_{5} (x) - lo g_{5} (x + 6) = 2

20 lo g_{10} (1 + x) = 0.1