What is 8.07428ln| P/((P-90))|-8.07428ln(4/41) ?

The solution to 8.07428ln| P/((P-90))|-8.07428ln(4/41) is ln((144832988.43409…P^8)/((P-90)^8))

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simplify 8.07428ln| P/((P-90))|-8.07428ln(4/41)

simplify

8.07428 ln \frac{P}{( P - 90 )} - 8.07428 ln (\frac{4}{41})

ln (\frac{144832988.43409 \dots P ^{8}}{( P - 90 ) ^{8}})

Solution steps

8.07428 ln \frac{P}{( P - 90 )} - 8.07428 ln (\frac{4}{41})

Apply log rule:

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

8.07428 ln \frac{P}{( P - 90 )} = ln (\frac{P}{( P - 90 )}^{8.07428})

= ln (\frac{P}{( P - 90 )}^{8.07428}) - 8.07428 ln (\frac{4}{41})

Apply log rule:

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

8.07428 ln (\frac{4}{41}) = ln ((\frac{4}{41})^{8.07428})

= ln (\frac{P}{( P - 90 )}^{8.07428}) - ln ((\frac{4}{41})^{8.07428})

Apply log rule:

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

ln (\frac{P}{( P - 90 )}^{8.07428}) - ln ((\frac{4}{41})^{8.07428}) = ln (\frac{\frac{P}{P - 90} ^{8.07428}}{( \frac{4}{41} ) ^{8.07428}})

= ln (\frac{\frac{P}{P - 90} ^{8.07428}}{( \frac{4}{41} ) ^{8.07428}})

Simplify

\frac{\frac{P}{( P - 90 )} ^{8.07428}}{( \frac{4}{41} ) ^{8.07428}} : \frac{144832988.43409 \dots P ^{8}}{( P - 90 ) ^{8}}

= ln (\frac{144832988.43409 \dots P ^{8}}{( P - 90 ) ^{8}})

- lo g_{10} (3.98 \cdot 1 0^{- 7})

3.14 + lo g_{10} (\frac{1.875}{0.625})

e ln (ey) - e - ln (y) + 1

ln (\frac{24}{74})

\frac{1}{\frac{1}{3} - 1} \cdot ln (\frac{0.75 - 1}{0.75 \cdot \frac{1}{3} - 1})

What is 8.07428ln| P/((P-90))|-8.07428ln(4/41) ?
The solution to 8.07428ln| P/((P-90))|-8.07428ln(4/41) is ln((144832988.43409…P^8)/((P-90)^8))