What is simplify-ln(5.4-3)+2ln(5.4-2) ?

The solution to simplify-ln(5.4-3)+2ln(5.4-2) is ln(4.81666…)

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simplify-ln(5.4-3)+2ln(5.4-2)

simplify

- ln (5.4 - 3) + 2 ln (5.4 - 2)

ln (4.81666 \dots)

Decimal

1.57208 \dots

Solution steps

- ln (5.4 - 3) + 2 ln (5.4 - 2)

Apply log rule:

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

2 ln (5.4 - 2) = ln ((5.4 - 2)^{2})

= - ln (5.4 - 3) + ln ((5.4 - 2)^{2})

Apply log rule:

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

ln ((5.4 - 2)^{2}) - ln (5.4 - 3) = ln (\frac{( 5.4 - 2 ) ^{2}}{5.4 - 3})

= ln (\frac{( 5.4 - 2 ) ^{2}}{5.4 - 3})

\frac{( 5.4 - 2 ) ^{2}}{5.4 - 3} = 4.81666 \dots

= ln (4.81666 \dots)

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

3 lo g_{7} (x) - 4 lo g_{7} (y)

ln (\frac{6.09}{9.42 \cdot 1 0 ^{- 3}}) \cdot 0.0002

ln (\frac{249}{3999})

ln (500) + 3 ln (\frac{575}{500})

What is simplify-ln(5.4-3)+2ln(5.4-2) ?
The solution to simplify-ln(5.4-3)+2ln(5.4-2) is ln(4.81666…)