What is the answer to log_{x+1}(x+3)=2 ?

The answer to log_{x+1}(x+3)=2 is x=1

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log_{x+1}(x+3)=2

lo g_{x + 1} (x + 3) = 2

x = 1

Solution steps

lo g_{x + 1} (x + 3) = 2

Apply log rules

\frac{ln ( x + 3 )}{ln ( x + 1 )} = 2

Multiply both sides by

ln (x + 1)

\frac{ln ( x + 3 )}{ln ( x + 1 )} ln (x + 1) = 2 ln (x + 1)

Simplify

ln (x + 3) = 2 ln (x + 1)

Apply log rules

x + 3 = (x + 1)^{2}

Solve

x + 3 = (x + 1)^{2} : x = 1, x = - 2

x = 1, x = - 2

Verify Solutions:

x = 1

True

, x = - 2

False

The solution is

x = 1

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

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ln (x) + ln (x + 4) = 3

0.67 = ln (y)

ln (3 x) + ln (2 x) = 9