What is 0.5ln(3/4)+3ln(1.5) ?

The solution to 0.5ln(3/4)+3ln(1.5) is ln(2.92283…)

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simplify 0.5ln(3/4)+3ln(1.5)

simplify

0.5 ln (\frac{3}{4}) + 3 ln (1.5)

ln (2.92283 \dots)

Decimal Notation

1.07255 \dots

Solution steps

0.5 ln (\frac{3}{4}) + 3 ln (1.5)

Apply log rule:

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

0.5 ln (\frac{3}{4}) = ln ((\frac{3}{4})^{0.5})

= ln ((\frac{3}{4})^{0.5}) + 3 ln (1.5)

Apply log rule:

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

3 ln (1.5) = ln (1. 5^{3})

= ln ((\frac{3}{4})^{0.5}) + ln (1. 5^{3})

Apply log rule:

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

ln ((\frac{3}{4})^{0.5}) + ln (1. 5^{3}) = ln (1. 5^{3} (\frac{3}{4})^{0.5})

= ln (1. 5^{3} (\frac{3}{4})^{0.5})

(\frac{3}{4})^{0.5} \cdot 1. 5^{3} = 2.92283 \dots

= ln (2.92283 \dots)

(\frac{3 ln ^{2} ( 3 x ) + 1}{x ( ln ^{3} ( 3 x ) + ln ( x ) )}) ln (x)

- 2 \cdot lo g_{10} (0.35) - lo g_{10} (0.17)

- lo g_{10} (2.41 \cdot 1 0^{- 3})

\frac{800 ( \frac{1}{60} )}{2 π ( 15 - 12 )} ln (\frac{10}{2})

ln (\frac{x}{27})

What is 0.5ln(3/4)+3ln(1.5) ?
The solution to 0.5ln(3/4)+3ln(1.5) is ln(2.92283…)