SOLUTION: 1) suppose that g(x) = 5^x - 3. a) what is g(0)? b) What point is on the graph of g? c) If g(x) = 622, what is the value of x? 2) Solve the logarithmic equation: 4e^(y+1) =

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 1) suppose that g(x) = 5^x - 3. a) what is g(0)? b) What point is on the graph of g? c) If g(x) = 622, what is the value of x? 2) Solve the logarithmic equation: 4e^(y+1) =       Log On


   

Question 691374: 1) suppose that g(x) = 5^x - 3.
a) what is g(0)?
b) What point is on the graph of g?
c) If g(x) = 622, what is the value of x?
2) Solve the logarithmic equation: 4e^(y+1) = 5
3) Write the given expression as a single logarithm:
21(log3)(third root of w)+(log3)(9w^2)-(log3)9
Completely lost and have no idea on how to do these. Help please.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1) suppose that g(x) = 5^x - 3.
a) what is g(0)?
g(0) = 5^0 - 3
any term with an exponent of 0 is equal to 1, therefore
g(0) = 1 - 3
g(0) = -2
:
b) What point is on the graph of g?
Let x = 2
g(2) = 5^2 - 3
g(2) = 25 - 3
g(2) = 22
Point 2, 22 is on the graph
:
c) If g(x) = 622, what is the value of x?
x = 622
:
2) Solve the logarithmic equation:
4e^(y+1) = 5
divide both sides by 4
e^(y+1) = 5/4
e^(y-1) = 1.25
Using nat logs
ln(e^(y-1) = ln(1.25)
The log equiv of exponent
(y-1)*ln(e) = ln(1.25)
the ln of e is one so we have
y - 1 = .223
y = .223 + 1
y = 1.223
Check this on your calc: enter: 4*e^(1.223-1), results: 4.999 ~ 5
:
3) Write the given expression as a single logarithm:
21(log3)(third root of w)+(log3)(9w^2)-(log3)9
Assume you mean:
21%2Alog%283%2Cw%5E%281%2F3%29%29%2Blog%283%2Cw%5E2%29-log%283%2C9%29
the exponent equiv
21%2Alog%283%2Cw%5E%2821%281%2F3%29%29%29%2Blog%283%2Cw%5E2%29-log%283%2C9%29 = log%283%2Cw%5E7%29%2Blog%283%2Cw%5E2%29-log%283%2C9%29
Adding logs is multiply, subtracting logs is divide
log%283%2C%28w%5E7%2Aw%5E2%29%2F9%29 = log%283%2C%28w%5E9%2F9%29%29