What is (98-10ln(16)+10ln(9))/7 ?

The solution to (98-10ln(16)+10ln(9))/7 is (98+10ln(9/16))/7

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simplify (98-10ln(16)+10ln(9))/7

simplify

\frac{98 - 10 ln ( 16 ) + 10 ln ( 9 )}{7}

\frac{98 + 10 ln ( \frac{9}{16} )}{7}

Decimal Notation

13.17805 \dots

Solution steps

\frac{98 - 10 ln ( 16 ) + 10 ln ( 9 )}{7}

Apply log rule:

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

10 ln (16) = ln (1 6^{10})

= \frac{98 - ln ( 1 6 ^{10} ) + 10 ln ( 9 )}{7}

Apply log rule:

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

10 ln (9) = ln (9^{10})

= \frac{98 - ln ( 1 6 ^{10} ) + ln ( 9 ^{10} )}{7}

Apply log rule:

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

ln (9^{10}) - ln (1 6^{10}) = ln (\frac{9 ^{10}}{1 6 ^{10}})

= \frac{98 + ln ( \frac{9 ^{10}}{1 6 ^{10}} )}{7}

ln (\frac{9 ^{10}}{1 6 ^{10}}) = 10 ln (\frac{9}{16})

= \frac{98 + 10 ln ( \frac{9}{16} )}{7}

lo g_{10} (\frac{x}{z ^{8}})

lo g_{5} (x^{2} - 2 x) + lo g_{5} (x^{- 1})

\frac{1}{5} ln (3) - \frac{1}{5} ln (8)

ln (\frac{x}{11})

lo g_{10} (x) + lo g_{10} (x^{2} - 25) - lo g_{10} (8) - lo g_{10} (x + 5)

What is (98-10ln(16)+10ln(9))/7 ?
The solution to (98-10ln(16)+10ln(9))/7 is (98+10ln(9/16))/7