What is the answer to log_{10}(x)-log_{10}(x-16)=2 ?

The answer to log_{10}(x)-log_{10}(x-16)=2 is x= 1600/99

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log_{10}(x)-log_{10}(x-16)=2

lo g_{10} (x) - lo g_{10} (x - 16) = 2

x = \frac{1600}{99}

Decimal Notation

x = 16.16161 \dots

Solution steps

lo g_{10} (x) - lo g_{10} (x - 16) = 2

Add

lo g_{10} (x - 16)

to both sides

lo g_{10} (x) - lo g_{10} (x - 16) + lo g_{10} (x - 16) = 2 + lo g_{10} (x - 16)

Simplify

lo g_{10} (x) = 2 + lo g_{10} (x - 16)

Apply log rules

x = 100 (x - 16)

Solve

x = 100 (x - 16) : x = \frac{1600}{99}

x = \frac{1600}{99}

Verify Solutions:

x = \frac{1600}{99}

True

The solution is

x = \frac{1600}{99}

72 = lo g_{x} (x)

lo g_{b} (50) = 1

x, ln (y) = ln (1 + x)

0.67 = lo g_{10} (x)

lo g_{10} (x - 15) = lo g_{10} (x)

What is the answer to log_{10}(x)-log_{10}(x-16)=2 ?
The answer to log_{10}(x)-log_{10}(x-16)=2 is x= 1600/99
Solve for x: log_{10}(x)-log_{10}(x-16)=2
The solution is x= 1600/99