What is 40e^9-15ln(19)+210+15ln(x) ?

The solution to 40e^9-15ln(19)+210+15ln(x) is 40e^9+ln((x^{15})/(19^{15)})+210

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simplify 40e^9-15ln(19)+210+15ln(x)

simplify

40 e^{9} - 15 ln (19) + 210 + 15 ln (x)

40 e^{9} + ln (\frac{x ^{15}}{1 9 ^{15}}) + 210

Solution steps

40 e^{9} - 15 ln (19) + 210 + 15 ln (x)

Apply log rule:

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

15 ln (19) = ln (1 9^{15})

= 40 e^{9} - ln (1 9^{15}) + 210 + 15 ln (x)

Apply log rule:

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

15 ln (x) = ln (x^{15})

= 40 e^{9} - ln (1 9^{15}) + 210 + ln (x^{15})

Apply log rule:

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

ln (x^{15}) - ln (1 9^{15}) = ln (\frac{x ^{15}}{1 9 ^{15}})

= 40 e^{9} + ln (\frac{x ^{15}}{1 9 ^{15}}) + 210

- lo g_{10} (1.09 \cdot 1 0^{- 3})

8.58 (1600 - 300) - (300 \cdot 8.58) ln (\frac{300}{1600})

\frac{1}{2} ln (x) + ln (c)

ln (\frac{2}{6})

What is 40e^9-15ln(19)+210+15ln(x) ?
The solution to 40e^9-15ln(19)+210+15ln(x) is 40e^9+ln((x^{15})/(19^{15)})+210