What is log_{10}(4)+3log_{10}(1.715) ?

The solution to log_{10}(4)+3log_{10}(1.715) is log_{10}(40353607/2000000)

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simplify log_{10}(4)+3log_{10}(1.715)

simplify

lo g_{10} (4) + 3 lo g_{10} (1.715)

lo g_{10} (\frac{40353607}{2000000})

Decimal Notation

1.30485 \dots

Solution steps

lo g_{10} (4) + 3 lo g_{10} (1.715)

Apply log rule:

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

3 lo g_{10} (1.715) = lo g_{10} (1.71 5^{3})

= lo g_{10} (4) + lo g_{10} (1.71 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} (1.71 5^{3}) = lo g_{10} (4 \cdot 1.71 5^{3})

= lo g_{10} (4 \cdot 1.71 5^{3})

4 \cdot 1.71 5^{3} = 20.1768035

= lo g_{10} (20.1768035)

20.1768035 = \frac{201768035}{10000000}

= lo g_{10} (\frac{201768035}{10000000})

Cancel

\frac{201768035}{10000000} : \frac{40353607}{2000000}

= lo g_{10} (\frac{40353607}{2000000})

ln (y e^{- n x})

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ln (5 b \frac{b + 1}{b - 1})

ln (\frac{1}{1 + x})

ln (3) - ln (1) + ln (2)

What is log_{10}(4)+3log_{10}(1.715) ?
The solution to log_{10}(4)+3log_{10}(1.715) is log_{10}(40353607/2000000)