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

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

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

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

x = 5

Solution steps

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

Add

lo g_{4} (x - 3)

to both sides

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

Simplify

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

Apply log rules

(x + 3) (x - 3) = 16

Solve

(x + 3) (x - 3) = 16 : x = 5, x = - 5

x = 5, x = - 5

Verify Solutions:

x = 5

True

, x = - 5

False

The solution is

x = 5

2 ln (b) = ln (289)

lo g_{e} (\frac{x}{1 - x}) = e^{2}

- 2.26 = lo g_{10} (x)

lo g_{16} (b) + lo g_{16} (b - 15) = 1

t, x = ln (4 t)

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