1. What is the exact solution to the equation e^{2x+1} = 7?
2. The parent function is f(x)=2^{x+3}-3 and the new function g(x)=2^{x+2}-1
How does the grah change from f(x) to g(x)
select each correct answer
The graph is shifted 1 unit right
The graph is shifted 2 units down
The graph is shifted 1 unit left
The graph is shifted 2 units up
3. Solve the sytem of equations using the substitution method
y=2+5/6x
4x-3y=3
thankies
1. e^(2x + 1) = 7 take the Ln of both sides
Ln e^(2x + 1) = Ln 7 and by a log property, we can write
(2x + 1) Ln e = Ln 7 since Ln e = 1, we can drop this
2x + 1 = Ln 7 subtract 1 from both sides
2x = Ln (7) - 1 divide both sides by 2
x = [ Ln (7) - 1 ] / 2 { third answer }
2.
The graph is shifted 1 unit right
The graph is shifted 2 units up
3.
y=2+5/6x
4x-3y=3
Sub the first equation into the second for y and we have
4x - 3 [ 2 + 5/6 x ] = 3 simplify
4x - 6 - 15/6 x = 3
4x - 6 - 5/2 x = 3 multiply through by 2 to clear the fraction
8x - 12 - 5x = 6
3x - 12 = 6 add 12 to both sides
3x = 18 divide both sides by 3
x = 6
And using y = 2 + 5/6 x ..... we can find y as
y = 2 + 5/6 (6) = 2 + 5 = 7