What is ln(128/49)-25ln(10/7)+9/2 ?

The solution to ln(128/49)-25ln(10/7)+9/2 is ln((7^{23})/(5^{25)*262144})+9/2

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simplify ln(128/49)-25ln(10/7)+9/2

simplify

ln (\frac{128}{49}) - 25 ln (\frac{10}{7}) + \frac{9}{2}

ln (\frac{7 ^{23}}{5 ^{25} \cdot 262144}) + \frac{9}{2}

Decimal Notation

- 3.45666 \dots

Solution steps

ln (\frac{128}{49}) - 25 ln (\frac{10}{7}) + \frac{9}{2}

Apply log rule:

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

25 ln (\frac{10}{7}) = ln ((\frac{10}{7})^{25})

= ln (\frac{128}{49}) - ln ((\frac{10}{7})^{25}) + \frac{9}{2}

Apply log rule:

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

ln (\frac{128}{49}) - ln ((\frac{10}{7})^{25}) = ln (\frac{\frac{128}{49}}{( \frac{10}{7} ) ^{25}})

= ln (\frac{\frac{128}{49}}{( \frac{10}{7} ) ^{25}}) + \frac{9}{2}

\frac{\frac{128}{49}}{( \frac{10}{7} ) ^{25}} = \frac{7 ^{23}}{5 ^{25} \cdot 262144}

= ln (\frac{7 ^{23}}{5 ^{25} \cdot 262144}) + \frac{9}{2}

- ln (6) + ln (5)

- \frac{3 ln ( 2 )}{4}

8.31 \cdot ln (0.7 5^{\frac{1}{0.35}} \cdot 4)

ln (10) - ln (- 1)

5 ln (0.2 + 10) - 5 ln (10)

What is ln(128/49)-25ln(10/7)+9/2 ?
The solution to ln(128/49)-25ln(10/7)+9/2 is ln((7^{23})/(5^{25)*262144})+9/2