Work Shown:
log(200) = log(2^3*5^2)
log(200) = log(2^3) + log(5^2)
log(200) = 3*log(2) + 2*log(5)
log(200) = 3*q + 2*p
log(200) = 2p + 3q
The log rules I used were
log(A*B) = log(A)+log(B)
log(A^B) = B*log(A)
The equivalent expression of log(200) is 2p + 3q
The logarithmic expression is given as:
[tex]\mathbf{log 200}[/tex]
Rewrite as:
[tex]\mathbf{log(200) = log (25 \times 8)}[/tex]
Express as exponents
[tex]\mathbf{log(200) = log (5^2 \times 2^3)}[/tex]
Split
[tex]\mathbf{log(200) = log (5^2) +log(2^3)}[/tex]
Apply law of logarithms
[tex]\mathbf{log(200) = 2log (5) +3log(2)}[/tex]
From the question;
log(5) = p and log(2) = q
So, we have:
[tex]\mathbf{log(200) = 2p +3q}[/tex]
Hence, the equivalent expression of log(200) is 2p + 3q
Read more about logarithmic expressions at:
https://brainly.com/question/9665281
