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

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

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

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

x = 2

Solution steps

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

Apply log rules

(x - 1) (x + 2) = 4

Solve

(x - 1) (x + 2) = 4 : x = 2, x = - 3

x = 2, x = - 3

Verify Solutions:

x = 2

True

, x = - 3

False

The solution is

x = 2

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

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

ln (x + 3) = 4

ln (x) = 8

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

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