Respuesta :
[tex]\bf \textit{logarithm of factors}\\\\
log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y)
\\\\\\
\textit{Logarithm of exponentials}\\\\
log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\
-------------------------------\\\\
4500\implies 6\cdot 6\cdot 5\cdot 5\cdot 5\implies 6^2\cdot 5^3
\\\\\\
ln(4500)\implies ln(6^2\cdot 5^3)\implies ln(6^2)+ln(5^3)\implies 2ln(6)+3ln(5)[/tex]
Simplified form of the given logarithmic expression ln(4500) will be ln(4500) = 3ln(5) + 2ln(6)
Given logarithmic expression in the question is,
- ln(4500)
We have to convert this expression in terms of ln(5) and ln(6).
Since, Factored form of 4500 = 5×5×5×6×6
= 5³×6²
Therefore, ln(4500) = ln(5³×6²)
= ln(5³) + ln(6²) [Since, ln(a × b) = ln(a) + ln(b)]
= 3ln(5) + 2ln(6) [Since, ln(a³) = 3ln(a)]
Hence, ln(4500) = 3ln(5) + 2ln(6) will be the answer.
Learn more,
https://brainly.com/question/282940
