What is log_{10}(40)-log_{10}(5) ?

The solution to log_{10}(40)-log_{10}(5) is 3log_{10}(2)

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simplify log_{10}(40)-log_{10}(5)

simplify

lo g_{10} (40) - lo g_{10} (5)

3 lo g_{10} (2)

Decimal Notation

0.90308 \dots

Solution steps

lo g_{10} (40) - lo g_{10} (5)

Apply log rule:

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

lo g_{10} (40) - lo g_{10} (5) = lo g_{10} (\frac{40}{5})

= lo g_{10} (\frac{40}{5})

Divide the numbers:

\frac{40}{5} = 8

= lo g_{10} (8)

Factor the number:

8 = 2^{3}

= lo g_{10} (2^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{10} (2^{3}) = 3 lo g_{10} (2)

= 3 lo g_{10} (2)

ln (\frac{3}{y})

(\frac{1}{2})^{3} - 24 ln (\frac{1}{2}) + 6

lo g_{15} (15 x)

ln (\frac{e x ^{4}}{y})

\frac{1}{2} lo g_{10} (a) + 6 lo g_{10} (b)

What is log_{10}(40)-log_{10}(5) ?
The solution to log_{10}(40)-log_{10}(5) is 3log_{10}(2)