SOLUTION: Find algebraic solutions for each system of equation b) y= 2(1/3)^(-x) and y=6(9)^(x+1) c) y= 1000(0.1)^(2x) and y=10^x thank you!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find algebraic solutions for each system of equation b) y= 2(1/3)^(-x) and y=6(9)^(x+1) c) y= 1000(0.1)^(2x) and y=10^x thank you!      Log On


   

Question 146747This question is from textbook Advanced Functions and Introductory Caculus
: Find algebraic solutions for each system of equation
b) y= 2(1/3)^(-x) and y=6(9)^(x+1)
c) y= 1000(0.1)^(2x) and y=10^x

thank you! This question is from textbook Advanced Functions and Introductory Caculus

Answer by nabla(475) About Me  (Show Source):
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b)
y=2(3)^x
y=6(9)(9)^x
So we want
2(3)^x=6(9)(9)^x
3^x=3(3^2)(3)^(2x)
3^x=3^(2x+3)
so x=2x+3
-3=x.
And y becomes y=2(3)^(-3)=2/27
c.
y=1000(.1)^(2x)
y=10^x
so we want
1000(.1)^(2x)=10^x
10^3(10^(-1))^(2x)=10^x
10^(-2x+3)=10^x
so -2x+3=x
and x=1
y becomes 10.