What is 5ln(a)+(ln(b))/3-3ln(c) ?

The solution to 5ln(a)+(ln(b))/3-3ln(c) is ln((a^5}{c^3})+\frac{ln(b))/3

Popular >

simplify 5ln(a)+(ln(b))/3-3ln(c)

simplify

5 ln (a) + \frac{ln ( b )}{3} - 3 ln (c)

ln (\frac{a ^{5}}{c ^{3}}) + \frac{ln ( b )}{3}

Solution steps

5 ln (a) + \frac{ln ( b )}{3} - 3 ln (c)

Apply log rule:

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

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

= ln (a^{5}) + \frac{ln ( b )}{3} - 3 ln (c)

Apply log rule:

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

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

= ln (a^{5}) + \frac{ln ( b )}{3} - ln (c^{3})

Apply log rule:

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

ln (a^{5}) - ln (c^{3}) = ln (\frac{a ^{5}}{c ^{3}})

= ln (\frac{a ^{5}}{c ^{3}}) + \frac{ln ( b )}{3}

ln (\frac{1}{72})

lo g_{10} (x) - \frac{1}{2} lo g_{10} (y) + 3 lo g_{10} (z)

lo g_{10} (\frac{x}{y})

ln (a) - ln (d) - ln (c)

lo g_{10} (100 x)

What is 5ln(a)+(ln(b))/3-3ln(c) ?
The solution to 5ln(a)+(ln(b))/3-3ln(c) is ln((a^5}{c^3})+\frac{ln(b))/3