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

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

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

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

x = 5

Solution steps

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

Move

lo g_{4} (2)

to the right side

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

Apply log rules

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

Solve

x - 3 = 4^{1 - \frac{1}{2}} : x = 5

x = 5

Verify Solutions:

x = 5

True

The solution is

x = 5

lo g_{2} (x) + lo g_{2} (4) = lo g_{2} (20)

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

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)

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