If log710≈1.183

Question

log
7
⁡
10
≈
1.183
and log720≈1.540
log
7
⁡
20
≈
1.540
, what is log7(10⋅20)
log
7
⁡
(
10
⋅
20
)
? Use the Product Rule of Logarithms to solve.(1 point)
Responses

1.822
1.822

0.357
0.357

2.723
2.723

1.302

Answer 1

To find ${\log }_7(10\cdot 20)$, we can use the Product Rule of Logarithms, which states that:

$${\log }_b(m\cdot n)={\log }_b(m)+{\log }_b(n)$$

In this case, we can express ${\log }_7(10\cdot 20)$ as:

$${\log }_7(10\cdot 20)={\log }_7(10)+{\log }_7(20)$$

We are given the approximate values of ${\log }_7(10)$ and ${\log }_7(20)$:

• ${\log }_7(10)\approx 1.183$
• ${\log }_7(20)\approx 1.540$

Now, substituting these values into the equation, we have:

$${\log }_7(10\cdot 20)\approx 1.183+1.540$$

Calculating this sum:

$$1.183+1.540=2.723$$

Thus, the value of ${\log }_7(10\cdot 20)$ is approximately $2.723$.

Therefore, the correct response is:

2.723