Finding the power using logarithm

[disregardthat]

Actually, I am trying to use what I have learned on school to something else

Homework Statement

3*10^x = 1.73*10^14

Homework Equations

lga^x = xlga

The Attempt at a Solution

10^x = (1.73 * 10^14)/3
10^x = 5.767 * 10^13
xlg10 = 13lg(57.67)

x=13lg(57.67)
x=22.89

:\

3 * 10^22.89 = 1.73 * 10^14 is certainly not correct..
What am I doing wrong?

I tried this too:
x=5.767 * 13lg(10)
x=5.767 * 13
x = 74.971

And that is even more incorrect!

 

[arildno]

Actually, I am trying to use what I have learned on school to something else

Homework Statement

3*10^x = 1.73*10^14

Homework Equations

lga^x = xlga

The Attempt at a Solution

10^x = (1.73 * 10^14)/3
10^x = 5.767 * 10^13
xlg10 = 13lg(57.67) HOW DID YOU GET YOUR RIGHT-HAND SIDE HERE?

Answer my question, please!

 

[disregardthat]

i know that if a=b, then lga = lgb
and lga^x=xlga

then i just took the ^13 on the other hand of lg.5.767*10, an made that 13lg5.767*10) and that is 13lg57.67

But if that is incorrect, I tryed it the other way underneath. How am I supposed to get the right answer?

EDIT: I found out the right answer now.

I took the lg(0.576*10^14) and that became 13.76

and 3*10^13,76 is approximately 1.73*10^14

 

[arildno]

Questions:

1. Do you see any difference between the expressions:
(5.767*10)^{13} and 5.767*(10^{13})?

2. Do you see any relevance of 1. to the issue at hand?

 

[disregardthat]

I saw the difference, and I got my answer correct.

What do you mean by the number 2. I didn't uderstand

 

[HallsofIvy]

He was asking you if you saw why that difference was important!

 

[disregardthat]

I saw the difference afterwards :)