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

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

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

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

x = 4

Solution steps

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

Apply log rules

(x + 4)^{2} = 16 x

Solve

(x + 4)^{2} = 16 x : x = 4

x = 4

Verify Solutions:

x = 4

True

The solution is

x = 4

lo g_{2} (\frac{x}{10000}) = 5

lo g_{10} (\frac{1}{1 - x}) = - 1

2 x - 2 + ln (x) = 0

2 lo g_{10} (x) = - 1

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

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