What is 3.2ln(4.92)-5ln(17.9) ?

The solution to 3.2ln(4.92)-5ln(17.9) is ln(0.00008…)

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simplify 3.2ln(4.92)-5ln(17.9)

simplify

3.2 ln (4.92) - 5 ln (17.9)

ln (0.00008 \dots)

Decimal Notation

- 9.32541 \dots

Solution steps

3.2 ln (4.92) - 5 ln (17.9)

Apply log rule:

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

3.2 ln (4.92) = ln (4.9 2^{3.2})

= ln (4.9 2^{3.2}) - 5 ln (17.9)

Apply log rule:

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

5 ln (17.9) = ln (17. 9^{5})

= ln (4.9 2^{3.2}) - ln (17. 9^{5})

Apply log rule:

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

ln (4.9 2^{3.2}) - ln (17. 9^{5}) = ln (\frac{4.9 2 ^{3.2}}{17. 9 ^{5}})

= ln (\frac{4.9 2 ^{3.2}}{17. 9 ^{5}})

\frac{4.9 2 ^{3.2}}{17. 9 ^{5}} = 0.00008 \dots

= ln (0.00008 \dots)

ln (4) - ln (\frac{7}{2})

- lo g_{10} (0.7 \cdot 1 0^{- 3})

ln ((2 x + 1) (x - 4))

lo g_{e} (5 x)

ln (\frac{e ^{2 y}}{2})

What is 3.2ln(4.92)-5ln(17.9) ?
The solution to 3.2ln(4.92)-5ln(17.9) is ln(0.00008…)