FLUENCY
1. Which of the following is not equivalent to log 36?
(1) log 2 + log18
(3) log 30+ log 6
(2) 2log 6
(4) log 4+ log 9

Equivalent expressions are expressions with equal values.

is not equivalent to

The original expression is given as:

Next, we text the options

Apply law of logarithms

Remove bracket

is equivalent to

Apply law of logarithms

Remove bracket

Hence,

is not equivalent to

Read more about equivalent expressions at:

link

The option (3). "log30 + log6"

Step-by-step explanation:

In order to find the option that is not equivalent to log(36) we will try to rewrite this log into each option by using the logarithmic properties. This is done below:

(1) We want to reach "log 2 + log 18". We have:

log(36) = log(2*18) = log(2) + log(18)

Therefore the first is equivalent to log(36)

(3) We want to reach "log (30) + log(6)".

If we try to make 36 into a product that has 6 in it, it'd be 6*6, therefore we can't rewrite log(36) as log(30) + log(6). So this is the option that we were looking for.

(2) We want to reach "2*log(6)". We have:

log(36) = log(6²) = 2*log(6)

Therefore it is equivalent to log(36).

(4) We want to reach "log(4) + log(9)". We have:

log(36) = log(4*9) = log(4) + log(9).

Therefore it is equivalent to log(36).