What is ln(t)+7ln(r)-6ln(t) ?

The solution to ln(t)+7ln(r)-6ln(t) is ln((r^7)/(t^5))

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simplify ln(t)+7ln(r)-6ln(t)

simplify

ln (t) + 7 ln (r) - 6 ln (t)

ln (\frac{r ^{7}}{t ^{5}})

Solution steps

ln (t) + 7 ln (r) - 6 ln (t)

Apply log rule:

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

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

= ln (t) + ln (r^{7}) - 6 ln (t)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (t) + ln (r^{7}) = ln (t r^{7})

= ln (t r^{7}) - 6 ln (t)

Apply log rule:

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

6 ln (t) = ln (t^{6})

= ln (t r^{7}) - ln (t^{6})

Apply log rule:

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

ln (t r^{7}) - ln (t^{6}) = ln (\frac{t r ^{7}}{t ^{6}})

= ln (\frac{t r ^{7}}{t ^{6}})

Cancel the common factor:

t

= ln (\frac{r ^{7}}{t ^{5}})

2 (1 - ln (3) + ln (2))

lo g_{2} (\frac{n}{3 ^{i}})

ln (2) + ln (\frac{4}{3})

\frac{2}{3} lo g_{4} (x) + lo g_{4} (y)

What is ln(t)+7ln(r)-6ln(t) ?
The solution to ln(t)+7ln(r)-6ln(t) is ln((r^7)/(t^5))