What is 2.99^2ln(1.04)-9ln(1.02) ?

The solution to 2.99^2ln(1.04)-9ln(1.02) is ln(1.18816…)

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simplify 2.99^2ln(1.04)-9ln(1.02)

simplify

2.9 9^{2} ln (1.04) - 9 ln (1.02)

ln (1.18816 \dots)

Decimal Notation

0.17241 \dots

Solution steps

2.9 9^{2} ln (1.04) - 9 ln (1.02)

Apply log rule:

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

2.9 9^{2} ln (1.04) = ln (1.0 4^{2.9 9^{2}})

= ln (1.0 4^{2.9 9^{2}}) - 9 ln (1.02)

Apply log rule:

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

9 ln (1.02) = ln (1.0 2^{9})

= ln (1.0 4^{2.9 9^{2}}) - ln (1.0 2^{9})

Apply log rule:

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

ln (1.0 4^{2.9 9^{2}}) - ln (1.0 2^{9}) = ln (\frac{1.0 4 ^{2.9 9^{2}}}{1.0 2 ^{9}})

= ln (\frac{1.0 4 ^{2.9 9^{2}}}{1.0 2 ^{9}})

\frac{1.0 4 ^{2.9 9^{2}}}{1.0 2 ^{9}} = 1.18816 \dots

= ln (1.18816 \dots)

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What is 2.99^2ln(1.04)-9ln(1.02) ?
The solution to 2.99^2ln(1.04)-9ln(1.02) is ln(1.18816…)