expand in simplest form. log base 5 of ab

Question

jim_thompson5910 · Answer

use the rule 

$$\Large \log_{b}(xy) = \log_{b}(x)+\log_{b}(y)$$

to get this

$$\Large \log_{5}(ab) = \log_{5}(a)+\log_{5}(b)$$

anonymous · Answer

what is the change of base formula?

jim_thompson5910 · Answer

the change of base formula is

$$\Large \log_{b}(x) = \frac{\log(x)}{\log(b)}$$

you could also state it using natural logs too

$$\Large \log_{b}(x) = \frac{\ln(x)}{\ln(b)}$$

since the logs on the right side can be of any allowed base (as long as they are the same base)

anonymous · Answer

so in this case log base 15 of 17 would 15 be b?

jim_thompson5910 · Answer

correct, b = 15 and x = 17

$$\Large \log_{b}(x) = \frac{\log(x)}{\log(b)}$$

$$\Large \log_{15}(17) = \frac{\log(17)}{\log(15)}$$

anonymous · Answer

i tried that and it said its not the answer:/

jim_thompson5910 · Answer

sounds like they want you to use a calculator to evaluate $\Large \frac{\log(17)}{\log(15)}$

anonymous · Answer

i dont have a fancy one

jim_thompson5910 · Answer

use google then

type in  "log(17)/log(15)" without quotes into google and it will show a calculator with the result inside

jim_thompson5910 · Answer

tell me what result you get so I can confirm

anonymous · Answer

1.04

jim_thompson5910 · Answer

you should have gotten 1.04621891533

jim_thompson5910 · Answer

if you round that to two decimal places, then you would go from 1.04621891533 to 1.05

anonymous · Answer

so would log base 13 of 15 be 0.947?

jim_thompson5910 · Answer

you have the fraction mixed up

jim_thompson5910 · Answer

log base 13 of 15 = log(15)/log(13) = ???

anonymous · Answer

ohh okay i got it. i did the next three. number 11. the hydrogen concentration [H+] in a certain cleaning compound is [H+]=3.7*10^-11. use the formula pH= -log[H+] to find the pH of the cleaning compound

jim_thompson5910 · Answer

you just need to evaluate 

-1*log(3.7 * 10^(-11))

anonymous · Answer

10.432?

anonymous · Answer

what is the properties of logarithms? i need it for log base 3 of 27- 2 log base 3 of 3

jim_thompson5910 · Answer

27 = 3^3

jim_thompson5910 · Answer

log(27) = log(3^3)

log(27) = 3*log(3)

jim_thompson5910 · Answer

I'm using the rule that log(x^y) = y*log(x)

anonymous · Answer

so 1.431

jim_thompson5910 · Answer

hmm let me think

jim_thompson5910 · Answer

$$\Large \log_{3}(27) - 2\log_{3}(3)$$


$$\Large \log_{3}(3^3) - 2\log_{3}(3)$$


$$\Large 3\log_{3}(3) - 2\log_{3}(3)$$


$$\Large 3*1 - 2*1$$


$$\Large 3 - 2$$


$$\Large 1$$


---------------------------------------


So,


$$\Large \log_{3}(27) - 2\log_{3}(3)=1$$

anonymous · Answer

okay i did 12-13... 14. write the following logarithm as a quotient of two common logarithms. Do not simplify. log base 2 of 15

jim_thompson5910 · Answer

use the change of base formula and tell me what you get

jim_thompson5910 · Answer

they don't want you to use a calculator

anonymous · Answer

log15/log2

jim_thompson5910 · Answer

yep or log(15)/log(2) 

and that's all they want

anonymous · Answer

expand the following. log base 8 of sqrt r+6/ s^2t^1/4

jim_thompson5910 · Answer

can you draw that out?

anonymous · Answer

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