What is log_{7}(13.3)+log_{7}(1.9) ?

The solution to log_{7}(13.3)+log_{7}(1.9) is 1+log_{7}(361/100)

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simplify log_{7}(13.3)+log_{7}(1.9)

simplify

lo g_{7} (13.3) + lo g_{7} (1.9)

1 + lo g_{7} (\frac{361}{100})

Decimal Notation

1.65969 \dots

Solution steps

lo g_{7} (13.3) + lo g_{7} (1.9)

lo g_{7} (13.3) = lo g_{7} (\frac{133}{10})

lo g_{7} (1.9) = lo g_{7} (\frac{19}{10})

= lo g_{7} (\frac{133}{10}) + lo g_{7} (\frac{19}{10})

Apply log rule:

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

lo g_{7} (\frac{133}{10}) + lo g_{7} (\frac{19}{10}) = lo g_{7} (\frac{133}{10} \cdot \frac{19}{10})

= lo g_{7} (\frac{133}{10} \cdot \frac{19}{10})

\frac{133}{10} \cdot \frac{19}{10} = \frac{2527}{100}

= lo g_{7} (\frac{2527}{100})

Apply log rule:

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

lo g_{7} (\frac{2527}{100}) = lo g_{7} (2527) - lo g_{7} (100)

= lo g_{7} (2527) - lo g_{7} (100)

lo g_{7} (2527) = 1 + 2 lo g_{7} (19)

lo g_{7} (100) = 2 lo g_{7} (10)

= 1 + 2 lo g_{7} (19) - 2 lo g_{7} (10)

2 lo g_{7} (19) = lo g_{7} (1 9^{2})

- 2 lo g_{7} (10) = - lo g_{7} (1 0^{2})

= 1 + lo g_{7} (1 9^{2}) - lo g_{7} (1 0^{2})

lo g_{7} (1 9^{2}) - lo g_{7} (1 0^{2}) = lo g_{7} (\frac{361}{100})

= 1 + lo g_{7} (\frac{361}{100})

ln (4) + ln (9)

lo g_{3} (7) + lo g_{3} (x) - 9 lo g_{3} (y)

ln (p) - ln (50 - p)

ln (\frac{0.038}{0.002})

\frac{1}{- 0.2} ln (\frac{\frac{1001}{76}}{90})

What is log_{7}(13.3)+log_{7}(1.9) ?
The solution to log_{7}(13.3)+log_{7}(1.9) is 1+log_{7}(361/100)