What is the answer to log_{4}(x-4)=1-log_{4}(x-7) ?

The answer to log_{4}(x-4)=1-log_{4}(x-7) is x=8

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log_{4}(x-4)=1-log_{4}(x-7)

lo g_{4} (x - 4) = 1 - lo g_{4} (x - 7)

x = 8

Solution steps

lo g_{4} (x - 4) = 1 - lo g_{4} (x - 7)

Add

lo g_{4} (x - 7)

to both sides

lo g_{4} (x - 4) + lo g_{4} (x - 7) = 1 - lo g_{4} (x - 7) + lo g_{4} (x - 7)

Simplify

lo g_{4} (x - 4) + lo g_{4} (x - 7) = 1

Apply log rules

(x - 4) (x - 7) = 4

Solve

(x - 4) (x - 7) = 4 : x = 8, x = 3

x = 8, x = 3

Verify Solutions:

x = 8

True

, x = 3

False

The solution is

x = 8

lo g_{6} (8 x) - 3 lo g_{6} (3) = 2

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

lo g_{x} (10) = 2

50 = 10.751 ln (x) + 62.069

lo g_{x} (4096) = 4

What is the answer to log_{4}(x-4)=1-log_{4}(x-7) ?
The answer to log_{4}(x-4)=1-log_{4}(x-7) is x=8
Solve for x: log_{4}(x-4)=1-log_{4}(x-7)
The solution is x=8