we'll use the same log cancellation rule, since this is pretty much the same thing as the other, just recall that ln = logₑ.
![\bf \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\stackrel{\textit{we'll use this one}}{\downarrow }}{a^{log_a x}=x} \\\\\\ \textit{logarithm of factors} \\\\ log_a(xy)\implies log_a(x)+log_a(y) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ln(x)+ln(5)=2\implies ln(x\cdot 5)=2\implies log_e(5x)=2 \\\\\\ e^{log_e(5x)}=e^2\implies 5x=e^2\implies x=\cfrac{e^2}{5}](https://tex.z-dn.net/?f=%20%5Cbf%20%5Ctextit%7BLogarithm%20Cancellation%20Rules%7D%0A%5C%5C%5C%5C%0Alog_a%20a%5Ex%20%3D%20x%5Cqquad%20%5Cqquad%20%5Cstackrel%7B%5Cstackrel%7B%5Ctextit%7Bwe%27ll%20use%20this%20one%7D%7D%7B%5Cdownarrow%20%7D%7D%7Ba%5E%7Blog_a%20x%7D%3Dx%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ctextit%7Blogarithm%20of%20factors%7D%0A%5C%5C%5C%5C%0Alog_a%28xy%29%5Cimplies%20log_a%28x%29%2Blog_a%28y%29%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0Aln%28x%29%2Bln%285%29%3D2%5Cimplies%20ln%28x%5Ccdot%205%29%3D2%5Cimplies%20log_e%285x%29%3D2%0A%5C%5C%5C%5C%5C%5C%0Ae%5E%7Blog_e%285x%29%7D%3De%5E2%5Cimplies%205x%3De%5E2%5Cimplies%20x%3D%5Ccfrac%7Be%5E2%7D%7B5%7D%20)
![\bf \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ln(x)-ln(5)=2\implies ln\left( \cfrac{x}{5} \right)=2\implies log_e\left( \cfrac{x}{5} \right)=2\implies e^{log_e\left( \frac{x}{5} \right)}=e^2 \\\\\\ \cfrac{x}{5}=e^2\implies x=5e^2](https://tex.z-dn.net/?f=%20%5Cbf%20%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0Aln%28x%29-ln%285%29%3D2%5Cimplies%20ln%5Cleft%28%20%5Ccfrac%7Bx%7D%7B5%7D%20%5Cright%29%3D2%5Cimplies%20log_e%5Cleft%28%20%5Ccfrac%7Bx%7D%7B5%7D%20%5Cright%29%3D2%5Cimplies%20e%5E%7Blog_e%5Cleft%28%20%5Cfrac%7Bx%7D%7B5%7D%20%5Cright%29%7D%3De%5E2%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7Bx%7D%7B5%7D%3De%5E2%5Cimplies%20x%3D5e%5E2%20)
Answer:
5/7
Step-by-step explanation:

Answer: 54
Step-by-step explanation:
First we add 17 plus 18 to dins total number of students I got 35
Then we make ratio
3/35
So we know we have total number of 630 kids then we make a ratio with no teacher so x
X/630
Lin both together then done ☑️
Step-by-step explanation:
The error carolyn has made is that she hasn't subtracted properly.
2x + 3y - (2x +6y) = 2x - 2x + 3y - 6y = -3y.
Carolyn probably didn't use parentheses...
To do the thing in substitution, we single out x or y in any equation. In this case, i'm gonna single out the x in the 2nd eqn. In other words, i'll make x the subject of the 2nd eqn.
2x + 6y = 10
2x = 10 - 6y
x = 5 - 3y
Now we simply plug in 5 - 3y wherever x apperas in the 1st equation.
2 (5-3y) + 3y = 8
10 - 6y + 3y = 8
10 - 3y = 8
-3y = -2
y = 2/3
Then x = 5 - 3*2/3 = 3
x=3
y=2/3
Hope it helps:)
1. Simplified already
2. 5x^2 x (3x+5)
3. 3x^3 x (3x^4 +11)