Respuesta :

Answer:

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).

MrRoyal

Equivalent expressions are expressions with equal values.

[tex]\mathbf{(b)\ log\ 30 + log\ 6}[/tex] is not equivalent to [tex]\mathbf{log\ 36}[/tex]

The original expression is given as:

[tex]\mathbf{log\ 36}[/tex]

Next, we text the options

[tex]\mathbf{(a)\ log\ 2 + log\ 18}[/tex]

Apply law of logarithms

[tex]\mathbf{log\ 2 + log\ 18 = log(2 \times 18)}[/tex]

[tex]\mathbf{log\ 2 + log\ 18 = log(36)}[/tex]

Remove bracket

[tex]\mathbf{log\ 2 + log\ 18 = log36}[/tex]

[tex]\mathbf{(a)\ log\ 2 + log\ 18}[/tex] is equivalent to [tex]\mathbf{log\ 36}[/tex]

[tex]\mathbf{(b)\ log\ 30 + log\ 6}[/tex]

Apply law of logarithms

[tex]\mathbf{log\ 30 + log\ 6 = log(30 \times 6)}[/tex]

[tex]\mathbf{log\ 30 + log\ 6 = log(180)}[/tex]

Remove bracket

[tex]\mathbf{log\ 30 + log\ 6 = log180}[/tex]

Hence,

[tex]\mathbf{(b)\ log\ 30 + log\ 6}[/tex] is not equivalent to [tex]\mathbf{log\ 36}[/tex]

Read more about equivalent expressions at:

https://brainly.com/question/24242989

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