What is the answer to log_{3}(x-4)+log_{3}(x+14)=5 ?

The answer to log_{3}(x-4)+log_{3}(x+14)=5 is x=13

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log_{3}(x-4)+log_{3}(x+14)=5

lo g_{3} (x - 4) + lo g_{3} (x + 14) = 5

x = 13

Solution steps

lo g_{3} (x - 4) + lo g_{3} (x + 14) = 5

Apply log rules

(x - 4) (x + 14) = 243

Solve

(x - 4) (x + 14) = 243 : x = 13, x = - 23

x = 13, x = - 23

Verify Solutions:

x = 13

True

, x = - 23

False

The solution is

x = 13

lo g_{2} (x) = 16

lo g_{4} (- 2 x + 8) = 3

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

lo g_{10} (x + 2) - 2 lo g_{10} (x) = 0

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

What is the answer to log_{3}(x-4)+log_{3}(x+14)=5 ?
The answer to log_{3}(x-4)+log_{3}(x+14)=5 is x=13
Solve for x: log_{3}(x-4)+log_{3}(x+14)=5
The solution is x=13