Question

Condense 1/2 log516 - 3 log5X + 4 log5Y a.log58y4/x3
b.log54 Y4/X3
c.1.5 log516Y/X
d.log5(4 - x3 + Y4)

Answer 1

here are some log laws that may help

1. Addition/Multiplication

\[\log _{a}m + \log _{a} n = \log _{a}(m timesn)... or... \log _{a}(mn)\]

2. Subtraction/Division

\[\log _{a}m - \log _{a} n = \log _{a}(\frac{m}{n})\]

3. Power

\[mlog _{a}n = \log _{a}(n^m)\]

start by using the power law

\[\log _{5} (16)^{\frac{1}{2}} - \log _{5}(x^3) + \log _{5}(y^4)\]

\[16^\frac{1}{2} = 4\]

next the addition and subtraction laws

\[\log _{5}(\frac{4}{x^3})+\log _{5}y^4\]

gives a final answer

\[\log _{5}(\frac{4y^4}{x^3})\]