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

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

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

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

x = 8

Solution steps

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

Add

lo g_{4} (x - 4)

to both sides

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

Simplify

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

Apply log rules

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

Solve

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

x = 8, x = 3

Verify Solutions:

x = 8

True

, x = 3

False

The solution is

x = 8

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

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

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

lo g_{a} (5) = - 2

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

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