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Popular >

simplify 5ln(2)+4ln(4)-4ln(5)

Solution

simplify

5 ln (2) + 4 ln (4) - 4 ln (5)

Solution

ln (\frac{8192}{625})

+1

Decimal Notation

2.57316 \dots

Solution steps

5 ln (2) + 4 ln (4) - 4 ln (5)

Apply log rule:

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

4 ln (4) = ln (4^{4})

= 5 ln (2) + ln (4^{4}) - 4 ln (5)

Apply log rule:

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

4 ln (5) = ln (5^{4})

= 5 ln (2) + ln (4^{4}) - ln (5^{4})

Apply log rule:

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

ln (4^{4}) - ln (5^{4}) = ln (\frac{4 ^{4}}{5 ^{4}})

= 5 ln (2) + ln (\frac{4 ^{4}}{5 ^{4}})

\frac{4 ^{4}}{5 ^{4}} = \frac{256}{625}

= 5 ln (2) + ln (\frac{256}{625})

Apply log rule:

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

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

= ln (2^{5}) + ln (\frac{256}{625})

Apply log rule:

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

ln (2^{5}) + ln (\frac{256}{625}) = ln (2^{5} \cdot \frac{256}{625})

= ln (2^{5} \cdot \frac{256}{625})

2^{5} \cdot \frac{256}{625} = \frac{8192}{625}

= ln (\frac{8192}{625})

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Frequently Asked Questions (FAQ)

What is 5ln(2)+4ln(4)-4ln(5) ?
The solution to 5ln(2)+4ln(4)-4ln(5) is ln(8192/625)