anonymous 3 years ago How does this simplification work? Can someone show me the intermediate steps?

1. anonymous

|dw:1346313632906:dw|

2. anonymous

$\ln(x)*(\frac{1}{x*\ln10})+\log(x)*(1/x)=\frac{2*\ln(x)}{x*\ln(x)}$

3. anonymous

Is this what you mean?

4. anonymous

Yes

5. anonymous

okay we will need to convert log(x) to ln(x) using a given equation

6. anonymous

we are doing this since there are no log(x) in the final answer

7. anonymous

$\log _{a}(x)=\frac{\ln(x)}{\ln(a)}$

8. anonymous

so for log base 10$\log _{10}(x)=\frac{\ln(x)}{\ln(10)}$

9. anonymous

go ahead and convert this in the expression above. see what you get.

10. anonymous

|dw:1346315335776:dw|

11. anonymous

|dw:1346315440405:dw|

12. anonymous

^ How did you get that? Isn't whatever you do to the top, you have to do to the bottom?

13. anonymous

you had forgotten the x in the denominator, i simply added it back

14. anonymous

$\frac{\ln(x)}{x*\ln(10)}+\frac{\log(x)}{x}=\frac{\ln(x)}{x*\ln(10)}+\frac{\ln(x)/\ln(10)}{x}$

15. anonymous

then move ln(10) to the denominator of the 2nd fraction

16. anonymous

where does the log (x) / x come from?

17. anonymous

from the original expression that you gave me. you wrote it as $\log(x)*\frac{1}{x}$

18. anonymous

$\log(x)*\frac{1}{x}=\frac{\log(x)}{x}$

19. anonymous

? |dw:1346316105596:dw| from this?

20. anonymous

yes, unless i was mistaken by what you wrote

21. anonymous

$\ln(x)*\frac{1}{x*\ln(10)}+\log(x)*\frac{1}{x}$ am i misunderstanding what you wrote?

22. anonymous

Ohh I see it, thank you!