What is log_{10}(18)-log_{10}(2) ?

The solution to log_{10}(18)-log_{10}(2) is 2log_{10}(3)

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simplify log_{10}(18)-log_{10}(2)

simplify

lo g_{10} (18) - lo g_{10} (2)

2 lo g_{10} (3)

Decimal Notation

0.95424 \dots

Solution steps

lo g_{10} (18) - lo g_{10} (2)

Apply log rule:

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

lo g_{10} (18) - lo g_{10} (2) = lo g_{10} (\frac{18}{2})

= lo g_{10} (\frac{18}{2})

Divide the numbers:

\frac{18}{2} = 9

= lo g_{10} (9)

Factor the number:

9 = 3^{2}

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

Apply log rule:

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

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

= 2 lo g_{10} (3)

- lo g_{10} (1.52 \cdot 1 0^{- 5})

5 ln (x - 6) - 4 ln (x)

lo g_{10} (18) - lo g_{10} (9)

ln (2 e^{8})

lo g_{2} (2 x) - lo g_{4} (x + 2)

What is log_{10}(18)-log_{10}(2) ?
The solution to log_{10}(18)-log_{10}(2) is 2log_{10}(3)