Question

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

Answer 1

a) 5/9

b) 7

c) 5

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) (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)(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