What is simplify-7ln(2)+3/4+3ln(5) ?

The solution to simplify-7ln(2)+3/4+3ln(5) is ln(125/128)+3/4

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simplify-7ln(2)+3/4+3ln(5)

simplify

- 7 ln (2) + \frac{3}{4} + 3 ln (5)

ln (\frac{125}{128}) + \frac{3}{4}

Solution steps

- 7 ln (2) + \frac{3}{4} + 3 ln (5)

Apply log rule:

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

7 ln (2) = ln (2^{7})

= - ln (2^{7}) + \frac{3}{4} + 3 ln (5)

Apply log rule:

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

3 ln (5) = ln (5^{3})

= - ln (2^{7}) + \frac{3}{4} + ln (5^{3})

Apply log rule:

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

ln (5^{3}) - ln (2^{7}) = ln (\frac{5 ^{3}}{2 ^{7}})

= ln (\frac{5 ^{3}}{2 ^{7}}) + \frac{3}{4}

\frac{5 ^{3}}{2 ^{7}} = \frac{125}{128}

= ln (\frac{125}{128}) + \frac{3}{4}

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What is simplify-7ln(2)+3/4+3ln(5) ?
The solution to simplify-7ln(2)+3/4+3ln(5) is ln(125/128)+3/4