What is ln(t)+5ln(p^2)-(ln(m))/3 ?

The solution to ln(t)+5ln(p^2)-(ln(m))/3 is ln(tp^{10})-(ln(m))/3

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simplify ln(t)+5ln(p^2)-(ln(m))/3

simplify

ln (t) + 5 ln (p^{2}) - \frac{ln ( m )}{3}

ln (t p^{10}) - \frac{ln ( m )}{3}

Solution steps

ln (t) + 5 ln (p^{2}) - \frac{ln ( m )}{3}

Apply log rule:

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

5 ln (p^{2}) = ln ((p^{2})^{5})

= ln (t) + ln ((p^{2})^{5}) - \frac{ln ( m )}{3}

Apply log rule:

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

ln (t) + ln ((p^{2})^{5}) = ln (t (p^{2})^{5})

= ln (t (p^{2})^{5}) - \frac{ln ( m )}{3}

(p^{2})^{5} = p^{10}

= ln (t p^{10}) - \frac{ln ( m )}{3}

lo g_{b} (\frac{x ^{3} y}{z ^{9}})

lo g_{4} (\frac{64}{x + 4})

lo g_{10} (51) - lo g_{10} (17)

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

ln (\frac{4}{9 x ^{9} y})

What is ln(t)+5ln(p^2)-(ln(m))/3 ?
The solution to ln(t)+5ln(p^2)-(ln(m))/3 is ln(tp^{10})-(ln(m))/3