Answer:
a) 5/9
b) 7
c) 5
Step-by-step explanation:
For a)
One of the rules for logs is that if there is a logarithm subtracted by a logarithm and they have the same base, it is the same as the log with the same base and the arguments are divided:
[tex]log_{x}z -log_{x} y[/tex] = [tex]log_{x} \frac{z}{y}[/tex]
so for this problem, they have the same base, so you can use this rule:
[tex]log_{4} 5-log_{4}9 = log_{4}\frac{5}{9}[/tex]
For b)
This is very similar, except instead of dividing the arguments, you want to multiply them.
So this is kind of saying "8 multiplied by x equals 56"
which is 7
For c)
If the argument has its own exponent, it can be brought to the front of the log like so:
[tex]log_{10}x^{y} = ylog_{10}x[/tex]
This one is a bit tricky because you have to actually set 32 into an exponent form first.
[tex]32 = 2^{5}[/tex]
Then we can bring that 5 in front of the logarithm
[tex]log_{6}2^{5} = 5log_{6}2[/tex]
So the answer is 5
