10.0k views
5 votes
Choose the single logarithm expression that is equivalent to the one shown!!! Help needed !!

A. Log 64
B. Log 12
C. Log 20
D. Log 10

Choose the single logarithm expression that is equivalent to the one shown!!! Help-example-1
User Laurence
by
5.2k points

2 Answers

4 votes

Answer:

A, log 64

Explanation:

your answer A, log 64 is correct. i will explain why below:

2 log 4, log 2 and log 2 have the same bases (10), meaning they are able to be added easier. but before we add, we use the Power Rule of Logarithms on 2 log 4

the Power Rule says that we can move an exponent in a logarithm to the front then solve. this also applies to the reverse, as we can move 2 back as an exponent of 4 and solve

2 log 4 ---> log 4² < simplify the exponent and we get log 16

we can now use the Product Rule of Logarithms where log x + log y = log(xy)

we can use that on the first two terms of the addition

log 16 + log 2 ----> log (16 × 2) = log 32

now we can apply the other log 2 to the rule but instead with log 32

log 32 + log 2 ---> log (32 × 2) = log 64

our answer is log 64

User Martin Algesten
by
5.2k points
1 vote

Answer:

log 64

Explanation:

Using the rules of logarithms

• log
x^(n) ⇔ nlogx

• logx + logy ⇔ log xy

Given

2 log 4 + log 2 + log 2

= log 4² + log (2 × 2)

= log 16 + log 4

= log (16 × 4) = log 64

User VolkA
by
4.9k points