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

The solution to simplify-ln(5)+4ln(2)-ln(3) is ln(16/15)

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

simplify

- ln (5) + 4 ln (2) - ln (3)

ln (\frac{16}{15})

Decimal Notation

0.06453 \dots

Solution steps

- ln (5) + 4 ln (2) - ln (3)

Apply log rule:

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

4 ln (2) = ln (2^{4})

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

Apply log rule:

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

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

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

2^{4} = 16

= ln (\frac{16}{5}) - ln (3)

Apply log rule:

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

ln (\frac{16}{5}) - ln (3) = ln (\frac{\frac{16}{5}}{3})

= ln (\frac{\frac{16}{5}}{3})

\frac{\frac{16}{5}}{3} = \frac{16}{15}

= ln (\frac{16}{15})

lo g_{7} (4 x)

\frac{1}{3} lo g_{c} (x) + 5 lo g_{c} (y) - 2 lo g_{c} (x)

\frac{1}{2} - 2 ln (\frac{1}{2})

lo g_{2} (3 x)

What is simplify-ln(5)+4ln(2)-ln(3) ?
The solution to simplify-ln(5)+4ln(2)-ln(3) is ln(16/15)