What is log_{10}(80)-0.3log_{10}(3) ?

The solution to log_{10}(80)-0.3log_{10}(3) is log_{10}(57.53784…)

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simplify log_{10}(80)-0.3log_{10}(3)

simplify

lo g_{10} (80) - 0.3 lo g_{10} (3)

lo g_{10} (57.53784 \dots)

Decimal Notation

1.75995 \dots

Solution steps

lo g_{10} (80) - 0.3 lo g_{10} (3)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

0.3 lo g_{10} (3) = lo g_{10} (3^{0.3})

= lo g_{10} (80) - lo g_{10} (3^{0.3})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (80) - lo g_{10} (3^{0.3}) = lo g_{10} (\frac{80}{3 ^{0.3}})

= lo g_{10} (\frac{80}{3 ^{0.3}})

\frac{80}{3 ^{0.3}} = 57.53784 \dots

= lo g_{10} (57.53784 \dots)

- lo g_{9} ((3 - x)^{2})

- lo g_{10} (6.31 \cdot 1 0^{- 3})

ln (\frac{0.010668}{0.007112})

ln (2 e) (\frac{5}{33})

ln (3 e^{2 θ})

What is log_{10}(80)-0.3log_{10}(3) ?
The solution to log_{10}(80)-0.3log_{10}(3) is log_{10}(57.53784…)