Logarithms?

Question

Can someone please explain to me how to do the following:

Solve:

y=log(base 3)(x-4)

e^(0.05t) = 3

e^(-x) = -1

And is lne equal to 1?

Thanks in advance!

Answer 1

Question 1
y = log3 (x - 4)
3^y = x - 4
x = 3^y + 4

Question 2
e ^ (0.05 t) = 3
(0.05 t) ln e = ln 3
0.05 t = ln 3
t = ln 3 / 0.05

Question 1
Undefined for real numbers.

Answer 2

Yes ln(e) = 1

to solve the first one you need to know that
log( base y) (x) = ln(x)/ln(y) where ln is a logrithm of any base

So the first one is y = ln(x-4)/ln(3) This is already solved for y, did you want to solve for x? Then you need to know that
y = log(base 3)(x-4) is just 3^y = x-4 and so x = 3^y+4

Similarly e^(0.05t) = 3, just take the ln of both sides to get
0.05t = ln(3) then t = ln(3)/0.05

The last one is

-x = ln(-1) which is undefined for real numbers - there may be a solution for complex numbers.