can someone help me out with these types of problems?

Question

1. solve for X in the following;
8^x = 32768

2. solvw for the approximate value of x in the following;
log x = 3

3. find the approximate value of X in the following
2 log x = log 8

4. solve for X
2^3x = 10

5.solve for X
3^x = 27

6. what is the value of X in the following;
Ln x = 4

7. find the value of X to two decimal places in the following;
Ln x = 3

8. solve for X
(log x)^3 = log x^3

Answer 1

just use your calculuator

log x = y means
10^y = x

e^y = x
means ln x = y

log x^c = c log x

Answer 2

1 take the log of both sides x*log(8) = log(32768) or x=log(32768)/log(8)

2. Take 10 to the power of each side 10^log(x) = 10^3
10^log(x) = x so x =10^3

3. Take 10 to the power of each side
x^2 =8 x = 2*sqrt(2)

4. Take 10 to the power of each side

x^2 = 10^log(8) so x = 10^(log(8)/2)

5. take log of both sides

3x*log(2) = log(27) so x =log(27)/[3*log(2)]

6. take e to the power of each side

x = e^4

7. Use your calculator.

8. (log x)^3 = log(x^3) = 3*log(x)

(log(x))^2= 3 --> log(x) = sqrt(3)

x = 10^sqrt(3)