What is (ln(5)+ln(5^2)+ln(3^3))/(ln(5)) ?

The solution to (ln(5)+ln(5^2)+ln(3^3))/(ln(5)) is (3ln(15))/(ln(5))

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simplify (ln(5)+ln(5^2)+ln(3^3))/(ln(5))

simplify

\frac{ln ( 5 ) + ln ( 5 ^{2} ) + ln ( 3 ^{3} )}{ln ( 5 )}

\frac{3 ln ( 15 )}{ln ( 5 )}

Decimal Notation

5.04781 \dots

Solution steps

\frac{ln ( 5 ) + ln ( 5 ^{2} ) + ln ( 3 ^{3} )}{ln ( 5 )}

Apply log rule:

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

ln (5^{2}) + ln (3^{3}) = ln (3^{3} \cdot 5^{2})

= \frac{ln ( 5 ) + ln ( 3 ^{3} \cdot 5 ^{2} )}{ln ( 5 )}

5^{2} \cdot 3^{3} = 675

= \frac{ln ( 5 ) + ln ( 675 )}{ln ( 5 )}

Apply log rule:

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

ln (5) + ln (675) = ln (5 \cdot 675)

= \frac{ln ( 5 \cdot 675 )}{ln ( 5 )}

Multiply the numbers:

5 \cdot 675 = 3375

= \frac{ln ( 3375 )}{ln ( 5 )}

Simplify

ln (3375) : 3 ln (15)

= \frac{3 ln ( 15 )}{ln ( 5 )}

ln (x^{3}) - ln (x^{2} + x)

\frac{13}{8} \cdot ln (\frac{13}{8}) - \frac{1}{\frac{13}{8}}

ln (2 \cdot 0.252)

ln (2 \frac{7 x ^{2}}{10})

- ln (\frac{40}{450})

What is (ln(5)+ln(5^2)+ln(3^3))/(ln(5)) ?
The solution to (ln(5)+ln(5^2)+ln(3^3))/(ln(5)) is (3ln(15))/(ln(5))