SOLUTION: Will someone please help me on these two problems. I was absent and have a test on them later today. 1. Use log5 2~0.4307 and log5 3~0.6826 to approximate the value of log5 12.

Question 167591: Will someone please help me on these two problems. I was absent and have a test on them later today.
1. Use log5 2~0.4307 and log5 3~0.6826 to approximate the value of log5 12.
2. Express log6 19 in terms of common logarithms. Then approximate its value to four decimal places.
I must show my work. Can you please help me through these
Thanks
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
1. Use log5 2~0.4307 and log5 3~0.6826 to approximate the value of log5 12.
.
So, instead of
log5(12)
we can write:
log5(2*2*3)
Applying log rule below:
logb(mn) = logb(m) + logb(n)
.
we get:
log5(2*2*3) = log5(2) + log5(2) + log5(3)
Now, we can substitute in the provided values:
log5(2*2*3) = 0.4307 + 0.4307 + 0.6826
log5(2*2*3) = 1.544
.
2. Express log6 19 in terms of common logarithms. Then approximate its value to four decimal places.
.
For this, we'll need to apply the change-of-base formula:
logb(x) = log(x)/log(b)
where "log" without a base indicates base 10.
.
So, now we can rewrite:
log6(19) = log(19)/log(6)
At this point, you'll need your calculator:
log6(19) = 1.27875/0.77815
log6(19) = 1.6433

RELATED QUESTIONS
Use log5(2)~.4307 and log5(3)~.6826 to approximate the expression without a calculator:... (answered by jim_thompson5910)

Will someone please help me. I don't know where to begin on this problem. I have to... (answered by monika_p)

I have two questions that I missed on a test. Will someone please help me. 1. The sum... (answered by Alan3354)

I need help with two more problems. They do not come from a book. I know the answers but... (answered by scott8148)

Could someone please help me with a few problems on the Elimination Method? 1) 5x - y = (answered by jim_thompson5910,scott8148)

I'm lost on these two problems. I have a test for a job tonight and need help to figure... (answered by Earlsdon,Nate)

use grouping to help solve the equation. 2r^3 + 3r^2 + 18r - 27. please i need to... (answered by richwmiller)

Well, i was absent and my teacher decided not to help me learn how to check Linear... (answered by fcabanski)

Hello, Can someone help me with these, I have some of the graphs but I not able to post... (answered by jim_thompson5910)