What is the answer to log_{4}(x-3)=-log_{4}(x-6)+1 ?

The answer to log_{4}(x-3)=-log_{4}(x-6)+1 is x=7

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log_{4}(x-3)=-log_{4}(x-6)+1

lo g_{4} (x - 3) = - lo g_{4} (x - 6) + 1

x = 7

Solution steps

lo g_{4} (x - 3) = - lo g_{4} (x - 6) + 1

Add

lo g_{4} (x - 6)

to both sides

lo g_{4} (x - 3) + lo g_{4} (x - 6) = - lo g_{4} (x - 6) + 1 + lo g_{4} (x - 6)

Simplify

lo g_{4} (x - 3) + lo g_{4} (x - 6) = 1

Apply log rules

(x - 3) (x - 6) = 4

Solve

(x - 3) (x - 6) = 4 : x = 7, x = 2

x = 7, x = 2

Verify Solutions:

x = 7

True

, x = 2

False

The solution is

x = 7

ln (3 x - 15) = 6

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

lo g_{x} (6) = \frac{1}{3}

ln (3 x - 15) = 5

ln (3 x - 15) = 3

What is the answer to log_{4}(x-3)=-log_{4}(x-6)+1 ?
The answer to log_{4}(x-3)=-log_{4}(x-6)+1 is x=7
Solve for x: log_{4}(x-3)=-log_{4}(x-6)+1
The solution is x=7