# How do you solve #log x - log(x-10)=1#?

Convert the logarithmic equation to an exponential equation.

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To solve the equation ( \log(x) - \log(x - 10) = 1 ), you can use the properties of logarithms.

- Start by applying the property ( \log(a) - \log(b) = \log\left(\frac{a}{b}\right) ):

[ \log(x) - \log(x - 10) = \log\left(\frac{x}{x - 10}\right) ]

- Set the equation equal to 1:

[ \log\left(\frac{x}{x - 10}\right) = 1 ]

- Convert the logarithmic equation into its exponential form:

[ 10^1 = \frac{x}{x - 10} ]

- Solve for ( x ):

[ 10 = \frac{x}{x - 10} ]

[ 10(x - 10) = x ]

[ 10x - 100 = x ]

[ 10x - x = 100 ]

[ 9x = 100 ]

[ x = \frac{100}{9} ]

So, the solution to the equation ( \log(x) - \log(x - 10) = 1 ) is ( x = \frac{100}{9} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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