What is (log_{10}(x+h)-log_{10}(x))/h ?

The solution to (log_{10}(x+h)-log_{10}(x))/h is (log_{10}((x+h)/x))/(h)

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simplify (log_{10}(x+h)-log_{10}(x))/h

simplify

\frac{lo g _{10} ( x + h ) - lo g _{10} ( x )}{h}

\frac{lo g _{10} ( \frac{x + h}{x} )}{h}

Solution steps

\frac{lo g _{10} ( x + h ) - lo g _{10} ( x )}{h}

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (x + h) - lo g_{10} (x) = lo g_{10} (\frac{x + h}{x})

= \frac{lo g _{10} ( \frac{x + h}{x} )}{h}

lo g_{4} (16 k^{8} x)

5 lo g_{2} (x) - 3 lo g_{2} (y)

lo g_{b} (\frac{x ^{4}}{z ^{2}})

2 (ln (x) - ln (x + 1) - ln (x - 1))

2 ln (x) + 3 ln (x + 1)

What is (log_{10}(x+h)-log_{10}(x))/h ?
The solution to (log_{10}(x+h)-log_{10}(x))/h is (log_{10}((x+h)/x))/(h)