Asked by hi

What is the first step in establishing that log(10^7⋅5) = 7+log 5 ?(1 point).

what is the answer.
Answered by hi
Evaluate log(10^4⋅10^3) .(1 point)

what is the answer.
Answered by hi
If log 4 7≈1.404 and log 4 5≈1.161 , what is log 4 35 ? Use the rule log b(xy)=log b x+log b y to solve.(1 point)

what is the answer.
Answered by hi
If ln 11 ≈ 2.398 and ln 5≈ 1.609 , what is ln 55 ? Use the Product Rule of Logarithms to solve.(1 point)

what is the answer.
Answered by hi
Which of the following correctly uses the Product Rule of Logarithms to find an equivalent expression to log 24? (1 point)

what is the answer.
Answered by GPT 3.5
The first step is to use the property of logarithms which states that log_a (b*c) = log_a (b) + log_a (c).

Using this property,
log(10^7*5) = log(10^7) + log(5).

Since log(10^7) = 7, the expression simplifies to:
7 + log(5).

Therefore, the answer is 7 + log(5).
Answered by GPT 3.5
Using the property of logarithms log_a (b*c) = log_a (b) + log_a (c), the expression can be written as:

log(10^4 * 10^3) = log(10^4) + log(10^3).

Since log(10^4) = 4 and log(10^3) = 3, the expression simplifies to:

4 + 3 = 7.

Therefore, the answer is 7.
Answered by GPT 3.5
Using the rule log_b(xy) = log_b(x) + log_b(y), we can write log_4(35) as:

log_4(35) = log_4(7*5).

Now we can use the given approximate values log_4(7) ≈ 1.404 and log_4(5) ≈ 1.161:

log_4(35) = log_4(7) + log_4(5).

Substituting the approximate values:

log_4(35) ≈ 1.404 + 1.161.

Adding the values:

log_4(35) ≈ 2.565.

Therefore, the approximate value of log_4(35) is 2.565.
Answered by GPT 3.5
To solve ln 55, we can use the product rule of logarithms, which states that ln (xy) = ln (x) + ln (y).

Using this rule, we can write ln 55 as:
ln 55 = ln (11*5).

Now we can use the given approximate values ln 11 ≈ 2.398 and ln 5 ≈ 1.609:

ln 55 = ln 11 + ln 5.

Substituting the approximate values:

ln 55 ≈ 2.398 + 1.609.

Adding the values:

ln 55 ≈ 4.007.

Therefore, the approximate value of ln 55 is 4.007.
Answered by GPT 3.5
To find an equivalent expression to log 24 using the Product Rule of Logarithms, we can split the number 24 into its factors. The Product Rule states that log (xy) = log(x) + log(y).

Out of the given options, the correct one that uses the Product Rule of Logarithms to find an equivalent expression to log 24 is:

log (3 * 8)

This can be further simplified using the Product Rule:
log 3 + log 8

So, the answer is log 3 + log 8.