What is log_{10}(80)-2*log_{10}(4) ?

The solution to log_{10}(80)-2*log_{10}(4) is log_{10}(5)

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simplify log_{10}(80)-2*log_{10}(4)

simplify

lo g_{10} (80) - 2 \cdot lo g_{10} (4)

lo g_{10} (5)

Decimal Notation

0.69897 \dots

Solution steps

lo g_{10} (80) - 2 lo g_{10} (4)

Apply log rule:

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

- 2 lo g_{10} (4) = - lo g_{10} (4^{2})

= lo g_{10} (80) - lo g_{10} (4^{2})

Apply log rule:

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

lo g_{10} (80) - lo g_{10} (4^{2}) = lo g_{10} (\frac{80}{4 ^{2}})

= lo g_{10} (\frac{80}{4 ^{2}})

Cancel

\frac{80}{4 ^{2}} : 5

= lo g_{10} (5)

lo g_{5} (\frac{x}{25 y ^{3}})

lo g_{10} (a) + 3 lo g_{10} (c)

- lo g_{10} (1.7 \cdot 1 0^{- 9})

lo g_{10} (x) + lo g_{10} (2)

2 lo g_{b} (4) + lo g_{b} (6)

What is log_{10}(80)-2*log_{10}(4) ?
The solution to log_{10}(80)-2*log_{10}(4) is log_{10}(5)