What is the answer to log_{10}(x+3)-log_{10}(x-3)=1 ?

The answer to log_{10}(x+3)-log_{10}(x-3)=1 is x= 11/3

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log_{10}(x+3)-log_{10}(x-3)=1

lo g_{10} (x + 3) - lo g_{10} (x - 3) = 1

x = \frac{11}{3}

Decimal Notation

x = 3.66666 \dots

Solution steps

lo g_{10} (x + 3) - lo g_{10} (x - 3) = 1

Add

lo g_{10} (x - 3)

to both sides

lo g_{10} (x + 3) - lo g_{10} (x - 3) + lo g_{10} (x - 3) = 1 + lo g_{10} (x - 3)

Simplify

lo g_{10} (x + 3) = 1 + lo g_{10} (x - 3)

Apply log rules

x + 3 = 10 (x - 3)

Solve

x + 3 = 10 (x - 3) : x = \frac{11}{3}

x = \frac{11}{3}

Verify Solutions:

x = \frac{11}{3}

True

The solution is

x = \frac{11}{3}

lo g_{10} (x^{2}) = 1.7482

2.3 lo g_{10} (\frac{t ^{1}}{t ^{2}}) = 0.69825

lo g_{10} (1 + x) = 1 + lo g_{10} (x)

ln (x + 1) = - 2

lo g_{2} (x) - lo g_{2} (x + 1) = 3

What is the answer to log_{10}(x+3)-log_{10}(x-3)=1 ?
The answer to log_{10}(x+3)-log_{10}(x-3)=1 is x= 11/3
Solve for x: log_{10}(x+3)-log_{10}(x-3)=1
The solution is x= 11/3