What is ln(70)+0.75ln(0.2362) ?

The solution to ln(70)+0.75ln(0.2362) is ln(23.71690…)

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simplify ln(70)+0.75ln(0.2362)

simplify

ln (70) + 0.75 ln (0.2362)

ln (23.71690 \dots)

Decimal Notation

3.16618 \dots

Solution steps

ln (70) + 0.75 ln (0.2362)

Apply log rule:

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

0.75 ln (0.2362) = ln (0.236 2^{0.75})

= ln (70) + ln (0.236 2^{0.75})

Apply log rule:

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

ln (70) + ln (0.236 2^{0.75}) = ln (70 \cdot 0.236 2^{0.75})

= ln (70 \cdot 0.236 2^{0.75})

70 \cdot 0.236 2^{0.75} = 23.71690 \dots

= ln (23.71690 \dots)

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What is ln(70)+0.75ln(0.2362) ?
The solution to ln(70)+0.75ln(0.2362) is ln(23.71690…)