What is 1/4 ln(45.83)+3/4 ln(53.8) ?

The solution to 1/4 ln(45.83)+3/4 ln(53.8) is ln(51.68614…)

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simplify 1/4 ln(45.83)+3/4 ln(53.8)

simplify

\frac{1}{4} ln (45.83) + \frac{3}{4} ln (53.8)

ln (51.68614 \dots)

Decimal Notation

3.94518 \dots

Solution steps

\frac{1}{4} ln (45.83) + \frac{3}{4} ln (53.8)

Apply log rule:

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

\frac{1}{4} ln (45.83) = ln (45.8 3^{\frac{1}{4}})

= ln (45.8 3^{\frac{1}{4}}) + \frac{3}{4} ln (53.8)

Apply log rule:

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

\frac{3}{4} ln (53.8) = ln (53. 8^{\frac{3}{4}})

= ln (45.8 3^{\frac{1}{4}}) + ln (53. 8^{\frac{3}{4}})

Apply log rule:

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

ln (45.8 3^{\frac{1}{4}}) + ln (53. 8^{\frac{3}{4}}) = ln (45.8 3^{\frac{1}{4}} \cdot 53. 8^{\frac{3}{4}})

= ln (45.8 3^{\frac{1}{4}} \cdot 53. 8^{\frac{3}{4}})

45.8 3^{\frac{1}{4}} \cdot 53. 8^{\frac{3}{4}} = 51.68614 \dots

= ln (51.68614 \dots)

lo g_{10} (7) + lo g_{10} (12) - lo g_{10} (3)

\frac{1}{4} ln (\frac{x ^{4} y ^{7}}{z ^{5}})

lo g_{10} (28) - lo g_{10} (14)

6 lo g_{10} (5) - lo g_{10} (2) - 3 lo g_{10} (3)

lo g_{4} (p^{2}) - lo g_{4} (4 q)

What is 1/4 ln(45.83)+3/4 ln(53.8) ?
The solution to 1/4 ln(45.83)+3/4 ln(53.8) is ln(51.68614…)