What is the answer to log_{4}(2/(x+3))=-1 ?

The answer to log_{4}(2/(x+3))=-1 is x=5

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log_{4}(2/(x+3))=-1

lo g_{4} (\frac{2}{x + 3}) = - 1

x = 5

Solution steps

lo g_{4} (\frac{2}{x + 3}) = - 1

Apply log rules

\frac{2}{x + 3} = 4^{- 1}

Multiply both sides by

x + 3

\frac{2}{x + 3} (x + 3) = 4^{- 1} (x + 3)

Simplify

4^{- 1} (x + 3) : \frac{1}{4} (x + 3)

2 = \frac{1}{4} (x + 3)

Solve

2 = \frac{1}{4} (x + 3) : x = 5

x = 5

Verify Solutions:

x = 5

True

The solution is

x = 5

lo g_{e} (x) = lo g_{10} (x)

2 (lo g_{8} (x) + lo g_{x} (8)) = 5

ln (x + 6) + ln (x - 2) = 2 ln (x)

ln (x) + ln (x + 6) = 4

lo g_{9} (x) = 0

What is the answer to log_{4}(2/(x+3))=-1 ?
The answer to log_{4}(2/(x+3))=-1 is x=5
Solve for x: log_{4}(2/(x+3))=-1
The solution is x=5