What is 2^0ln(2)-3^0ln(3) ?

The solution to 2^0ln(2)-3^0ln(3) is ln(2/3)

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simplify 2^0ln(2)-3^0ln(3)

simplify

2^{0} ln (2) - 3^{0} ln (3)

ln (\frac{2}{3})

Decimal Notation

- 0.40546 \dots

Solution steps

2^{0} ln (2) - 3^{0} ln (3)

Apply log rule:

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

2^{0} ln (2) = ln (2^{2^{0}})

= ln (2^{2^{0}}) - 3^{0} ln (3)

Apply log rule:

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

3^{0} ln (3) = ln (3^{3^{0}})

= ln (2^{2^{0}}) - ln (3^{3^{0}})

Apply log rule:

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

ln (2^{2^{0}}) - ln (3^{3^{0}}) = ln (\frac{2 ^{2^{0}}}{3 ^{3^{0}}})

= ln (\frac{2 ^{2^{0}}}{3 ^{3^{0}}})

\frac{2 ^{2^{0}}}{3 ^{3^{0}}} = \frac{2}{3}

= ln (\frac{2}{3})

lo g_{5} (x) - lo g_{5} (x^{4})

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lo g_{7} (9 x)

ln (x^{7} 6 - x)

ln (\frac{0.25}{0.22})