What is the answer to log_{2}(x-5)=3-log_{2}(x-7) ?

The answer to log_{2}(x-5)=3-log_{2}(x-7) is x=9

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log_{2}(x-5)=3-log_{2}(x-7)

lo g_{2} (x - 5) = 3 - lo g_{2} (x - 7)

x = 9

Solution steps

lo g_{2} (x - 5) = 3 - lo g_{2} (x - 7)

Add

lo g_{2} (x - 7)

to both sides

lo g_{2} (x - 5) + lo g_{2} (x - 7) = 3 - lo g_{2} (x - 7) + lo g_{2} (x - 7)

Simplify

lo g_{2} (x - 5) + lo g_{2} (x - 7) = 3

Apply log rules

(x - 5) (x - 7) = 8

Solve

(x - 5) (x - 7) = 8 : x = 9, x = 3

x = 9, x = 3

Verify Solutions:

x = 9

True

, x = 3

False

The solution is

x = 9

ln (x) + ln (x - 1) = ln (6)

lo g_{16} (x) = (lo g_{4} (x))^{2}

lo g_{10} (x) = 7

ln (y) = 0

ln (x + 1) + ln (x) = ln (6)

What is the answer to log_{2}(x-5)=3-log_{2}(x-7) ?
The answer to log_{2}(x-5)=3-log_{2}(x-7) is x=9
Solve for x: log_{2}(x-5)=3-log_{2}(x-7)
The solution is x=9