$5^{x-2}-7^{x-3}=7^{x-5}+11\cdot5^{x-4}\\\\5^{x-2}-7^{x-2-1}=7^{x-2-3}+11\cdot5^{x-2-2}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\5^{x-2}-\dfrac{7^{x-2}}{7^1}=\dfrac{7^{x-2}}{7^3}+11\cdot\dfrac{5^{x-2}}{5^2}\\\\5^{x-2}-\dfrac{1}{7}\cdot7^{x-2}=\dfrac{1}{343}\cdot7^{x-2}+\dfrac{11}{25}\cdot5^{x-2}\\\\-\dfrac{1}{7}\cdot7^{x-2}-\dfrac{1}{343}\cdot7^{x-2}=\dfrac{11}{25}\cdot5^{x-2}-5^{x-2}\\\\\left(-\dfrac{1}{7}-\dfrac{1}{343}\right)\cdot7^{x-2}=\left(\dfrac{11}{25}-1\right)\cdot5^{x-2}$

$\left(-\dfrac{49}{343}-\dfrac{1}{343}\right)\cdot7^{x-2}=-\dfrac{14}{25}\cdot5^{x-2}\\\\-\dfrac{50}{343}\cdot7^{x-2}=-\dfrac{14}{25}\cdot5^{x-2}\qquad\text{multiply both sides by}\ \left(-\dfrac{25}{14}\right)\\\\\dfrac{50\cdot25}{343\cdot14}\cdot7^{x-2}=5^{x-2}\qquad\text{divide both sides by}\ 7^{x-2}\\\\\dfrac{25\cdot25}{343\cdot7}=\dfrac{5^{x-2}}{7^{x-2}}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}$

$\dfrac{5^2\cdot5^2}{7^3\cdot7}=\left(\dfrac{5}{7}\right)^{x-2}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\\dfrac{5^4}{7^4}=\left(\dfrac{5}{7}\right)^{x-2}\\\\\left(\dfrac{5}{7}\right)^4=\left(\dfrac{5}{7}\right)^{x-2}\iff x-2=4\qquad\text{add 2 to both sides}\\\\\boxed{x=6}$

6 0

3 years ago

Read 2 more answers

Please solve equations by completing square

BlackZzzverrR [31]

$x^2-4x+1=0\\
x^2-4x+4-3=0\\
(x-2)^2=3\\
|x-2|=\sqrt3\\
x-2=\sqrt3 \vee x-2=-\sqrt3\\
x=2+\sqrt3 \vee x=2-\sqrt3$

$x^2+6x-9=0\\
x^2+6x+9-18=0\\
(x+3)^2=18\\
|x+3|=\sqrt{18}=3\sqrt2\\
x+3=3\sqrt2 \vee x+3=-3\sqrt2\\
x=-3+3\sqrt2 \vee x=-3-3\sqrt2\\$

$x^2+20x+3=0\\
x^2+20x+100-97=0\\
(x+10)^2=97\\
|x+10|=\sqrt{97}\\
x+10=\sqrt{97} \vee x+10=-\sqrt{97}\\
x=-10+\sqrt{97} \vee x=-10-\sqrt{97}$

$x^2-2x-5=0\\
x^2-2x+1-6=0\\
(x-1)^2=6\\
|x-1|=\sqrt6\\
x-1=\sqrt6 \vee x-1=-\sqrt6\\
x=1+\sqrt6 \vee x=1-\sqrt6$

8 0

4 years ago

A planter weighs 2 pounds and holds 3 pounds of soil. write two equivalent expressions for the total weight of nine planters. th

Anastasy [175]

Planters = (2*9)+(3*9) = 45 the answer is 45

5 0

3 years ago