What is the answer to log_{8}(x+4)-log_{8}(x-3)=1 ?

The answer to log_{8}(x+4)-log_{8}(x-3)=1 is x=4

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log_{8}(x+4)-log_{8}(x-3)=1

lo g_{8} (x + 4) - lo g_{8} (x - 3) = 1

x = 4

Solution steps

lo g_{8} (x + 4) - lo g_{8} (x - 3) = 1

Add

lo g_{8} (x - 3)

to both sides

lo g_{8} (x + 4) - lo g_{8} (x - 3) + lo g_{8} (x - 3) = 1 + lo g_{8} (x - 3)

Simplify

lo g_{8} (x + 4) = 1 + lo g_{8} (x - 3)

Apply log rules

x + 4 = 8 (x - 3)

Solve

x + 4 = 8 (x - 3) : x = 4

x = 4

Verify Solutions:

x = 4

True

The solution is

x = 4

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

lo g_{8} ((x - 3)^{9}) = 6

ln (4 - x^{2}) = 0

2 ln (x) - 2 ln (2) = ln (9)

lo g_{6} (x) + lo g_{6} (x) - 9 = 2

What is the answer to log_{8}(x+4)-log_{8}(x-3)=1 ?
The answer to log_{8}(x+4)-log_{8}(x-3)=1 is x=4
Solve for x: log_{8}(x+4)-log_{8}(x-3)=1
The solution is x=4