What is the answer to log_{4}(x+10)+log_{4}(x-5)=2 ?

The answer to log_{4}(x+10)+log_{4}(x-5)=2 is x=6

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log_{4}(x+10)+log_{4}(x-5)=2

lo g_{4} (x + 10) + lo g_{4} (x - 5) = 2

x = 6

Solution steps

lo g_{4} (x + 10) + lo g_{4} (x - 5) = 2

Apply log rules

(x + 10) (x - 5) = 16

Solve

(x + 10) (x - 5) = 16 : x = 6, x = - 11

x = 6, x = - 11

Verify Solutions:

x = 6

True

, x = - 11

False

The solution is

x = 6

lo g_{2} (x^{2} - 16) = 0

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

2 ln (x) - ln (x + 5) + ln (3) = ln (x)

ln (3 x + 6) + ln (2) = ln (63)

ln (2 - 3 x) = 9

What is the answer to log_{4}(x+10)+log_{4}(x-5)=2 ?
The answer to log_{4}(x+10)+log_{4}(x-5)=2 is x=6
Solve for x: log_{4}(x+10)+log_{4}(x-5)=2
The solution is x=6