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Popular >

simplify 1+ln(2^5)-5ln(5/2)

Solution

simplify

1 + ln (2^{5}) - 5 ln (\frac{5}{2})

Solution

1 + ln (\frac{1024}{3125})

+1

Decimal Notation

- 0.11571 \dots

Solution steps

1 + ln (2^{5}) - 5 ln (\frac{5}{2})

Apply log rule:

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

5 ln (\frac{5}{2}) = ln ((\frac{5}{2})^{5})

= 1 + ln (2^{5}) - ln ((\frac{5}{2})^{5})

Apply log rule:

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

ln (2^{5}) - ln ((\frac{5}{2})^{5}) = ln (\frac{2 ^{5}}{( \frac{5}{2} ) ^{5}})

= 1 + ln (\frac{2 ^{5}}{( \frac{5}{2} ) ^{5}})

\frac{2 ^{5}}{( \frac{5}{2} ) ^{5}} = \frac{1024}{3125}

= 1 + ln (\frac{1024}{3125})

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Frequently Asked Questions (FAQ)

What is 1+ln(2^5)-5ln(5/2) ?
The solution to 1+ln(2^5)-5ln(5/2) is 1+ln(1024/3125)