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

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

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

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

x = 7

Solution steps

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

Add

lo g_{4} (x - 3)

to both sides

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

Simplify

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

Apply log rules

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

Solve

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

x = 7, x = 2

Verify Solutions:

x = 7

True

, x = 2

False

The solution is

x = 7

ln (x + 1) + ln (x - 1) = 3

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

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

ln (x) = - 0.123

(ln (x))^{2} - ln (x^{3}) - 8 = 2

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