Question

Select all the correct answers.

Which expressions are equivalent to the given expression?

5 log2o+ log10 20 – log10 10

o logo(100x) + 1

log, (2.1)

log2:5)

o log10 (10r)

o log10 (2005) – 1

Answer 1

To find which expressions are equivalent to 5 log2o + log10 20 - log10 10, we can simplify each expression and compare the results.

Step-by-step explanation:

To find which expressions are equivalent to 5 log2o + log10 20 - log10 10, we can simplify each expression and compare the results.

1. 5 log2o can be simplified to log2(o^5).
2. log10 20 can be simplified to log10(2 * 10), which is equal to log10(2) + log10(10) = 1 + 1 = 2.
3. log10 10 can be simplified to 1.

Putting it all together, the expression becomes log2(o^5) + 2 - 1 = log2(o^5) + 1.

Therefore, the expressions that are equivalent to the given expression are: log2(o^5) + 1 and log10 (2005) - 1.

Answer 2

The correct equivalent expression to 5 log1020 + log1020 − log1010 is log10 (200), after simplifying the given expression using properties of logarithms such as product, quotient, and power rules.

Step-by-step explanation:

The question requires us to determine which expressions are equivalent to the given expression, 5 log1020 + log1020 − log1010. Utilizing the properties of logarithms, we can simplify the expression:

5 log1020 is equivalent to log10205 due to the power rule of logarithms (logb(an) = n logba).

The logarithm of a product (logb(xy) = logbx + logby) helps us combine the first two terms.

Subtracting log1010 from the sum uses the quotient rule of logarithms (logb(x/y) = logbx − logby).

The result simplifies to log10(205/10).

We can now match this result with the answer choices given. From the options provided:

log10 (200) is equivalent to log10 (205) − log10 10, thus is an equivalent expression.

The other expressions provided do not simplify to this final form and are therefore incorrect.