Question

1/2 log516 - 3 log5X + 4 log5Y

Answer 1

Is this your question
\[\frac 12 \log_ 5 16- 3\log_ 5 x+ 4\log_ 5 y\]
Do you want to simplify it?

Answer 2

yes

Answer 3

\[\log_{5}16^{1/2} -\log_{5}x ^{3} +\log_{5}y ^{4} =\log_{5}\sqrt{16} -\log_{5}x ^{3} +\log_{5}y ^{4} \]
\[\log_{4}4 -\log_{4}x ^{3} +\log_{4}y ^{4} =1+\log_{4}y^{4} -\log_{4} x ^{3}=1+\log_{4}(y ^{4}/x ^{3} ) \]

Answer 4

Logarithms are exponents. Adding exponents is the same as multiplying powers.

Answer 5

\[\log_{5} (4y^4/x^3)\]

Answer 6

yes sorry about changing the 5 to 4 as a base

Answer 7

Just remember properties of exponents and the fact that logarithms are exponents and you can't go wrong.
power * power, add the exponents/logarithms
power / power, subtract the exponents/logarithms
power^power, multiply the exponents/logarithms

and vice-versa if going in the inverse direction.

Answer 8

thanks do you also understand the natural log
ln and e