=log x^5+log x^(2×3)
=log x^5+ log x^6
The given logarithmic expression is:
This is the same as:
We now apply the product rule to get:
We now apply the power rule to get;
Given the logarithmic expression
Logarithm rule: when we take log with any number raise to power x
Then the power x move down before the log and write log with the base of number
For example : Let we take a number
When we take log then power x go down and write before the log and take log with the given base of that number
Therefore we can write as x log 2
Now , we have logarithmic expression
=Hence, the logarithmic expression is equivalent to .
A, log 64
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
C. log2 3/2.
When you are adding two logs with the same base, you multiply.
So, log2 6 + log2 2 = log2 6 * 2 = log2 12
When you subtract two logs with the same base, you divide.
So, log2 12 - log2 8 = log2 12 / 8 = log2 3/2
The answer is C. log2 3/2.
Hope this helps!!
correct answer comes out to be option A.
log₁₀60 - log₁₀10
using identity of logarithm
logₐb - logₐc =
log₁₀60 - log₁₀10 =
the equivalent of the given logarithmic expression comes out to be log₁₀ 6
hence, the correct answer comes out to be option A.
Using the rules of logarithms
• log ⇔ nlogx
• logx + logy ⇔ log xy
2 log 4 + log 2 + log 2
= log 4² + log (2 × 2)
= log 16 + log 4
= log (16 × 4) = log 64
Option c is correct
Using the logarithmic rules:
Given the expression:
Apply the logarithmic rules:
Apply the logarithmic rules we have;
Therefore, the single logarithmic expression that is equivalent to the one shown is,
The answer is A. log(8/7)
send it over