can somone please show me how these types are prblems are done? As best they can.?

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

Hi,

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

x log 8 = log 32768
x = log 32768/log 8
x = 5

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

Since the base of log is 10, this can be re-written into exponential form as:

10³ = x
1000 = x

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

log x² = log 8

x² = 8
x = 2.828

4. solve for X
2^3x = 10
3x log 2 = log 10
3x log 2 = 1
x = 1/(3log 2)
x = 1.107

5.solve for X
3^x = 27
x = 3 since 3³ = 27

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

Since Ln uses a base of "e", then exponential form for this equation would be e^4 = x.
x = 54.598

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

Since Ln uses a base of "e", then exponential form for this equation would be e^3 = x.
x = 20.086

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

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

(log x)² = 3
√(log x)² = √3
log x = √3

Since the base of log is 10, this can be re-written into exponential form as:

10^√3 = x
53.957 = x



I hope those help!! :-)

Answer 2

use the properties of logs:


1. solve for X in the following;
8^x = 32768
log(8^x) = log(32768)
x log8 = log(32768)
x= log(32768)/log8

2. solvw for the approximate value of x in the following;
log x = 3
10^{logx} = 10^3
x = 1000

3. find the approximate value of X in the following
2 log x = log 8
log x^2 = log 8
so x^2 =8
x= sqrt(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
e^{lnx} = e^3
x=e^3

Answer 3

1. since 8^x=32768=8^5 then x=5
2. 10^logx=10^3 so x=1000
3. 2logx=logx^2=log8 so x^2=8 so x=2*sqrt2
4. taking log of both sides 3xlog2=log10=1 x=1/(3log2)
5. 3^x=27=3^3 so x=3
6. Make both sides the power of e to get e^(Lnx)=e^4 so x=e^4
7. just like #6 x=e^3 use a calculator to find numeric value
8. logx logx logx = 3 logx so logx logx=3 so logx= 3^.5
so 10^logx=10^3.5 so x=10^(SQRT3)