What is the answer to log_{2}(x-5)=log_{4}(x-2)+log_{2}(2) ?

The answer to log_{2}(x-5)=log_{4}(x-2)+log_{2}(2) is x=11

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log_{2}(x-5)=log_{4}(x-2)+log_{2}(2)

lo g_{2} (x - 5) = lo g_{4} (x - 2) + lo g_{2} (2)

x = 11

Solution steps

lo g_{2} (x - 5) = lo g_{4} (x - 2) + lo g_{2} (2)

Apply log rules

(x - 5)^{2} = (x - 2) \cdot 4

Solve

(x - 5)^{2} = (x - 2) \cdot 4 : x = 11, x = 3

x = 11, x = 3

Verify Solutions:

x = 11

True

, x = 3

False

The solution is

x = 11

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

lo g_{3} (lo g_{\frac{1}{2}} (x) - 3 \cdot lo g_{\frac{1}{2}} (x) + 5) = 2

lo g_{10} (x^{2}) - 1 = lo g_{10} (3 x)

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

lo g_{4} (2 x - 32) = 5

What is the answer to log_{2}(x-5)=log_{4}(x-2)+log_{2}(2) ?
The answer to log_{2}(x-5)=log_{4}(x-2)+log_{2}(2) is x=11
Solve for x: log_{2}(x-5)=log_{4}(x-2)+log_{2}(2)
The solution is x=11