Logartithic Help?

Question

Could anyone figure out the answer to these problem and explain how they arrive at the answer..Ty...I'm having a hard time

Find the number:

1.) 10^log3
2.) log 10^5
3.) log 100
4.) log 0.0001
5.) e^ln 2
6.) ln e^-3
7.) e^2+ln 3
8.) 10^log 7

Answer 1

If log is base 10,
2)log 10^5 = 5 x log10 = 5x1= 5
3)log 10^2 = 2 x log10 = 2x1 =2
4)log 10^-4 = -4 x1 = -4
I think you should use a calculator for the rest.

Answer 2

1.) 10^log3 = 3
2.) log 10^5 = 5
3.) log 100 = 2
4.) log 0.0001 = -4
5.) e^ln 2 = 2
6.) ln e^-3 = -3
7.) e^2+ln 3 =(e^2)(3)
8.) 10^log 7 = 7

Answer 3

1.) 10^log3 = 3 because we have A^log b[base A] = b
2.) log 10^5 =5 * log 10 = 5
3.) log 100 = log 10^2 = 2* log 10 = 2
4.) log 10^-4 = -4 * log 10 = -4
5.) e^ln 2 = 2
6.) ln e^-3= -3*ln e = -3
7.) e^2+ln 3 if you mean e^(2+ln 3)= e^2xe^ln 3 = 3(e^2) otherwise it is in simpleset form
8.) 10^log 7 = 7

Answer 4

Before I begin, let me just state that b^ and log[base b] are inverses of each other, so that b^(log[base b](x)) = x and
log[base b](b^x) = x {for defined values of x}.

1) 10^(log3)

Remember that by default, log is equivalent to log[base 10]. Therefore, by the above explanation,

10^(log(3)) = 3

2) log 10^5

Again, by the above explanation, this is 5.

3) log 100
100 can be expressed as 10^2.
log(10^2), or 2

4) log (0.0001).

0.0001 = 10^(-4)

log(10^(-4)) = -4

5) e^ln(2) = 2, since e and ln are inverses of each other.

6) ln e^(-3) = -3

7) e^[2 + ln(3)]

First, split this up into two; remember that x^(a + b) is the same as (x^a)(x^b).

(e^2)(e^(ln(3)).
(e^2) (3)
3e^2

8) 10^log(7) = 7

Answer 5

1. 3
2. 5
3. 2
4. -4
5. 2
6. -3
7. can't be simplified anymore
8. 7

10^log(a), log 10^a, and same with ln cancels out...it's part of a list of logarithmic properties.

Answer 6

1) a^(log b)= b^l(og a)
10^log3=3^log10=3^1=3

2) log(a^b)=b log a
log10^5=5log10=5

3)log 100=log 10^2=2

4)log 0.0001=log 10^(-4)=-4

5)e^ln2=2^lne=2^1=2

6)ln e^-3=-3

7)i assume it is e^(2+ln3)
e^(a+b)=e^a*e^b
e^2*e^ln3=e^2*3^lne=3e^2

8)10^log7=7