Question

Anybody know this thankyou for any help!!!!!!

Answer 1

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:

$log_{x}z -log_{x} y$ = $log_{x} \frac{z}{y}$

so for this problem, they have the same base, so you can use this rule:

$log_{4} 5-log_{4}9 = log_{4}\frac{5}{9}$

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:

$log_{10}x^{y} = ylog_{10}x$

This one is a bit tricky because you have to actually set 32 into an exponent form first.

$32 = 2^{5}$

Then we can bring that 5 in front of the logarithm

$log_{6}2^{5} = 5log_{6}2$

So the answer is 5