What is 4log_{10}(3)-4log_{10}(8) ?

The solution to 4log_{10}(3)-4log_{10}(8) is log_{10}(81/4096)

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simplify 4log_{10}(3)-4log_{10}(8)

simplify

4 lo g_{10} (3) - 4 lo g_{10} (8)

lo g_{10} (\frac{81}{4096})

Decimal Notation

- 1.70387 \dots

Solution steps

4 lo g_{10} (3) - 4 lo g_{10} (8)

4 lo g_{10} (3) = lo g_{10} (3^{4})

- 4 lo g_{10} (8) = - lo g_{10} (8^{4})

= lo g_{10} (3^{4}) - lo g_{10} (8^{4})

Apply log rule:

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

lo g_{10} (3^{4}) - lo g_{10} (8^{4}) = lo g_{10} (\frac{3 ^{4}}{8 ^{4}})

= lo g_{10} (\frac{3 ^{4}}{8 ^{4}})

\frac{3 ^{4}}{8 ^{4}} = \frac{81}{4096}

= lo g_{10} (\frac{81}{4096})

ln (\frac{10}{3})

ln (2) + ln (x)

lo g_{2} (6 x)

lo g_{10} (x) - \frac{1}{2} lo g_{10} (y) + 4 lo g_{10} (z)

tanh (\frac{1}{2} lo g_{10} (\frac{1 + z}{1 - z}))

What is 4log_{10}(3)-4log_{10}(8) ?
The solution to 4log_{10}(3)-4log_{10}(8) is log_{10}(81/4096)