What is the answer to log_{7}(x+7)-log_{7}(x-5)=1 ?

The answer to log_{7}(x+7)-log_{7}(x-5)=1 is x=7

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log_{7}(x+7)-log_{7}(x-5)=1

lo g_{7} (x + 7) - lo g_{7} (x - 5) = 1

x = 7

Solution steps

lo g_{7} (x + 7) - lo g_{7} (x - 5) = 1

Add

lo g_{7} (x - 5)

to both sides

lo g_{7} (x + 7) - lo g_{7} (x - 5) + lo g_{7} (x - 5) = 1 + lo g_{7} (x - 5)

Simplify

lo g_{7} (x + 7) = 1 + lo g_{7} (x - 5)

Apply log rules

x + 7 = 7 (x - 5)

Solve

x + 7 = 7 (x - 5) : x = 7

x = 7

Verify Solutions:

x = 7

True

The solution is

x = 7

10 \cdot lo g_{10} (x) = 22.9

10 lo g_{10} (x) = 5

0 = 10 \cdot lo g_{10} (x)

0.63 = lo g_{10} (x)

3 = lo g_{5} (x)

What is the answer to log_{7}(x+7)-log_{7}(x-5)=1 ?
The answer to log_{7}(x+7)-log_{7}(x-5)=1 is x=7
Solve for x: log_{7}(x+7)-log_{7}(x-5)=1
The solution is x=7