What is log_{10}(4)-log_{10}(24) ?

The solution to log_{10}(4)-log_{10}(24) is -log_{10}(6)

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simplify log_{10}(4)-log_{10}(24)

simplify

lo g_{10} (4) - lo g_{10} (24)

- lo g_{10} (6)

Decimal Notation

- 0.77815 \dots

Solution steps

lo g_{10} (4) - lo g_{10} (24)

Apply log rule:

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

lo g_{10} (4) - lo g_{10} (24) = lo g_{10} (\frac{4}{24})

= lo g_{10} (\frac{4}{24})

Cancel the numbers:

\frac{4}{24} = \frac{1}{6}

= lo g_{10} (\frac{1}{6})

\frac{1}{6} = 6^{- 1}

= lo g_{10} (6^{- 1})

Apply log rule:

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

lo g_{10} (6^{- 1}) = - 1 \cdot lo g_{10} (6)

= - 1 \cdot lo g_{10} (6)

Apply rule:

1 \cdot a = a

= - lo g_{10} (6)

f (x) = lo g_{10} (3 x + 9) + lo g_{10} (x + 8)

lo g_{\frac{1}{3}} (3 x)

ln (5) - ln (20)

10 lo g_{10} (2) + lo g_{10} (3) - 3 lo g_{10} (4)

- \frac{6}{11} lo g_{2} (\frac{6}{11}) - \frac{5}{11} lo g_{2} (\frac{5}{11})

What is log_{10}(4)-log_{10}(24) ?
The solution to log_{10}(4)-log_{10}(24) is -log_{10}(6)