What is 3/2 ln(a)+1/2 ln(b)-1 ?

The solution to 3/2 ln(a)+1/2 ln(b)-1 is ln(a^{3/2}b^{1/2})-1

Popular >

simplify 3/2 ln(a)+1/2 ln(b)-1

simplify

\frac{3}{2} ln (a) + \frac{1}{2} ln (b) - 1

ln (a^{\frac{3}{2}} b^{\frac{1}{2}}) - 1

Solution steps

\frac{3}{2} ln (a) + \frac{1}{2} ln (b) - 1

Apply log rule:

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

\frac{3}{2} ln (a) = ln (a^{\frac{3}{2}})

= ln (a^{\frac{3}{2}}) + \frac{1}{2} ln (b) - 1

Apply log rule:

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

\frac{1}{2} ln (b) = ln (b^{\frac{1}{2}})

= ln (a^{\frac{3}{2}}) + ln (b^{\frac{1}{2}}) - 1

Apply log rule:

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

ln (a^{\frac{3}{2}}) + ln (b^{\frac{1}{2}}) = ln (a^{\frac{3}{2}} b^{\frac{1}{2}})

= ln (a^{\frac{3}{2}} b^{\frac{1}{2}}) - 1

2 lo g_{b} (w) + 4 (lo g_{b} (x) - 5 lo g_{b} (z))

lo g_{6} (\frac{x ^{3}}{y ^{6}})

lo g_{2} (\frac{15}{y})

lo g_{2} (x) + lo g_{2} (x + 15) + lo g_{2} (16)

2 lo g_{3} (6) - lo g_{3} (8)

What is 3/2 ln(a)+1/2 ln(b)-1 ?
The solution to 3/2 ln(a)+1/2 ln(b)-1 is ln(a^{3/2}b^{1/2})-1