What is log_{10}(4)+3log_{10}(0.235) ?

The solution to log_{10}(4)+3log_{10}(0.235) is log_{10}(103823/2000000)

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simplify log_{10}(4)+3log_{10}(0.235)

simplify

lo g_{10} (4) + 3 lo g_{10} (0.235)

lo g_{10} (\frac{103823}{2000000})

Decimal Notation

- 1.28473 \dots

Solution steps

lo g_{10} (4) + 3 lo g_{10} (0.235)

Apply log rule:

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

3 lo g_{10} (0.235) = lo g_{10} (0.23 5^{3})

= lo g_{10} (4) + lo g_{10} (0.23 5^{3})

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (4) + lo g_{10} (0.23 5^{3}) = lo g_{10} (4 \cdot 0.23 5^{3})

= lo g_{10} (4 \cdot 0.23 5^{3})

4 \cdot 0.23 5^{3} = 0.0519115

= lo g_{10} (0.0519115)

0.0519115 = \frac{519115}{10000000}

= lo g_{10} (\frac{519115}{10000000})

Cancel

\frac{519115}{10000000} : \frac{103823}{2000000}

= lo g_{10} (\frac{103823}{2000000})

ln (\frac{1}{0.4})

ln (\frac{1}{3}) - ln (x)

- \frac{1}{9} ln (- 2)

ln (\frac{1}{58})

ln (\frac{5}{18})

What is log_{10}(4)+3log_{10}(0.235) ?
The solution to log_{10}(4)+3log_{10}(0.235) is log_{10}(103823/2000000)