The solution of the logarithms equation is ![\rm log_5(25x^6\sqrt[3]{x^2+6}})](https://tex.z-dn.net/?f=%5Crm%20log_5%2825x%5E6%5Csqrt%5B3%5D%7Bx%5E2%2B6%7D%7D%29)
Given
The following expression:
![\rm 2log_5(5x^3)+\dfrac{1}{3}log_5(x^2+6)](https://tex.z-dn.net/?f=%5Crm%202log_5%285x%5E3%29%2B%5Cdfrac%7B1%7D%7B3%7Dlog_5%28x%5E2%2B6%29)
<h3>What properties for Logarithms are used to solve the equation?</h3>
The following properties are used in the logarithms equation given below.
![\rm loga+logb=logab\\\\ loga-logb=log(\dfrac{a}{b})\\\\ loga^n=nloga](https://tex.z-dn.net/?f=%5Crm%20loga%2Blogb%3Dlogab%5C%5C%5C%5C%20loga-logb%3Dlog%28%5Cdfrac%7Ba%7D%7Bb%7D%29%5C%5C%5C%5C%20loga%5En%3Dnloga)
According to the Power of a power property:
- Step 1: Apply the third property for logarithms shown above:
![\rm 2log_5(5x^3)+\dfrac{1}{3}log_5(x^2+6)\\\\\rm log_5(5x^3)^2+\log_5(x^2+6)^{\frac{1}{3}}](https://tex.z-dn.net/?f=%5Crm%202log_5%285x%5E3%29%2B%5Cdfrac%7B1%7D%7B3%7Dlog_5%28x%5E2%2B6%29%5C%5C%5C%5C%5Crm%20log_5%285x%5E3%29%5E2%2B%5Clog_5%28x%5E2%2B6%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
- Step 2: Apply the Power of a power property:
![\rm log_5(5x^3)^2+\log_5(x^2+6)^{\frac{1}{3}}\\\\log_5(25x^6)+log_5(\sqrt[3]{x^2+6}})](https://tex.z-dn.net/?f=%5Crm%20%20log_5%285x%5E3%29%5E2%2B%5Clog_5%28x%5E2%2B6%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5C%5C%5C%5Clog_5%2825x%5E6%29%2Blog_5%28%5Csqrt%5B3%5D%7Bx%5E2%2B6%7D%7D%29)
- Step 3: Using the property for Radicals;
![\rm log_5(25x^6)+log_5(\sqrt[3]{x^2+6}})\\\\ log_5(25x^6\sqrt[3]{x^2+6}})](https://tex.z-dn.net/?f=%5Crm%20log_5%2825x%5E6%29%2Blog_5%28%5Csqrt%5B3%5D%7Bx%5E2%2B6%7D%7D%29%5C%5C%5C%5C%20log_5%2825x%5E6%5Csqrt%5B3%5D%7Bx%5E2%2B6%7D%7D%29)
Hence, the solution of the logarithms equation is
.
To know more about logarithms properties click the link given below.
brainly.com/question/26053315
100/2 = 50 pies per hour
350/50 = 7 hours
p(x) = 90 / (9 + 50 * e^(-x))
e = 2.718, so we can use e = 2.7 as a quick substitute
p(3) =>
90 / (9 + 50 * e^(-3)) =>
90 / (9 + 50 * 2.7^(-3)) =>
90 / (9 + 50 / 2.7^3) =>
90 / ((9 * 2.7^3 + 50) / 2.7^3) =>
90 * 2.7^3 / (9 * 2.7^3 + 50)
2.7^3 =>
(27/10)^3 =>
27^3 / 1000 =>
729 * 27 / 1000 =>
2187 * 9 / 1000 =>
6561 * 3 / 1000 =>
19683 / 1000 =>
19.683
90 * 2.7^3 / (9 * 2.7^3 + 50) =>
90 * 19.683 / (9 * 19.683 + 50)
9 * 19.683 =>
9 * (20 - 0.317) =>
180 - 9 * 0.317 =>
180 - 9 * 0.3 - 9 * 0.017 =>
180 - 2.7 - 9 * 0.01 - 9 * 0.007 =>
177.3 - 0.09 - 0.063 =>
177.3 - 0.153 =>
177.15 - 0.003 =>
177.147
90 * 19.683 / (9 * 19.683 + 50) =>
10 * 177.147 / (177.147 + 50) =>
1771.47 / 227.147 =>
1771470 / 227147 =>
1770000 / 225000 =>
1770/225 =>
4 * 1770 / 900 =>
4 * 177 / 90 =>
708/90 =>
70.8 / 9 =>
23.6 / 3 =>
(21 + 2.6) / 3 =>
7 + 0.866666.... =>
7.8666666...
Actual value: 7.8333389811057471507345888320992.....
Not bad for some estimates, is it?
So this means that ABC is equal to PQR.
Therefore if AB is equal to PQ and BC is equal to QR.
I believe that the answer is AC = PR