SOLUTION: So the question is as follows: "If log 2 + 0.301 and log 3 + 0.447, find each of the following using only these values and the properties of logarithms. Show your work. a. lo

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Question 1012071: So the question is as follows:
"If log 2 + 0.301 and log 3 + 0.447, find each of the following using only these values and the properties of logarithms. Show your work.
a. log 6
b. log (2/3)
c. log 1.5
d. log 18"
my teacher stopped teaching the lessons because we have a limited time before exams, so she started assigning videos to watch. I watched the assigned ones, and many more but I just don't understand the question, I don't even really know what it's asking me to do.
Found 4 solutions by ankor@dixie-net.com, jim_thompson5910, ValorousDawn, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
I think it should read:
"If log 2 = 0.301 and log 3 + 0.477, find each of the following using only these values and the properties of logarithms.
a. log 6
log(2*3) = log(2)+log(3), when multiplying two numbers you add their logs
therefore
log(6) = .301+.447 = .778
:
b. log (2/3) when dividing you subtract their logs
log(2/3) = log(2) - log(3)
log(2/3) = .301 - .477 = -.156
:
c. log 1.5
1.5 = (3/2)
log(3/2) = .477 - .301 = .176
:
d. log 18"
same as , when raising a power you multiply log by the exponent
log(18) = 2(.477) + .301 = .954 + .301 = 1.255
:
Did this give you some idea of what is going here?

Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
I'm assuming you meant to write this

log(2) = 0.301
log(3) = 0.477

I used a calculator to compute those above

--------------------------------------------------------------------

We will use these log rules

(1)

(2)

(3)

--------------------------------------------------------------------
a)

log(6) = log(2*3)

log(6) = log(2) + log(3) ... Use rule 1 (see above)

log(6) = 0.301 + 0.477

log(6) = 0.778

--------------------------------------------------------------------
b)

log(2/3) = log(2) - log(3) ... Use rule 2 (see above)

log(2/3) = 0.301 - 0.477

log(2/3) = -0.176

--------------------------------------------------------------------
c)

log(1.5) = log(3/2)

log(1.5) = log(3) - log(2) ... Use rule 2 (see above)

log(1.5) = 0.477 - 0.301

log(1.5) = 0.176

--------------------------------------------------------------------
d)

log(18) = log(2*9)

log(18) = log(2*3^2)

log(18) = log(2)+log(3^2) ... Use rule 1 (see above)

log(18) = log(2)+2*log(3) ... Use rule 3 (see above)

log(18) = 0.301 + 2*0.477

log(18) = 1.255

All answers are approximate

Answer by ValorousDawn(53)   (Show Source):
You can put this solution on YOUR website!
Hi there. I'm sorry to hear about your situation, let me try my best.
Luckily, there's not a lot you have to know for these problems, but here's what you do have to know.

With this, we can tackle the problems.
Six is really just 2 times 3, so . We have from our first identity that , so . We know these values, and we can then use substitution. .

The second one is easier, as 2/3 is really straightforward. We use the identity here. We plug in a as 2 and b as 3 because they are the numerator and denominator respectively. We get . Then we can use substitution of values to solve. .

Don't get tricked up on the third one because it's a decimal, remember that 1.5 is the same thing as 3/2 in fractional form. . We use the same identity as above. .

This one's a bit harder, but we just have to go back to the basics. Factorize, and you'll get . Therefore, . We can break it apart. We get , which due to , becomes . Substitute in your values, and you're done.

Answer by MathTherapy(10556)   (Show Source):
You can put this solution on YOUR website!
So the question is as follows:
"If log 2 + 0.301 and log 3 + 0.447, find each of the following using only these values and the properties of logarithms. Show your work.
a. log 6
b. log (2/3)
c. log 1.5
d. log 18"
my teacher stopped teaching the lessons because we have a limited time before exams, so she started assigning videos to watch. I watched the assigned ones, and many more but I just don't understand the question, I don't even really know what it's asking me to do.

a.
I guess you meant: log 2 = .0301 ; and log 3 = 0.477 i/o log 3 = log 6 log 6 = log 2 * 3 log 6 = log 2 + log 3 ---- Applying log ab = log a + log b log 6 = .301 + .477 ------ Substituting given values of log 2 and log 3

b.
---- Applying = log a - log b ---- Substituting given values of log 2 and log 3

c.
log 1.5 --------> ----- Applying = log a - log b = .477 - .301 --- Substituting given values of log 2 and log 3

d.
log 18 ------->
log 18 = ----- Applying log ab = log a + log b
log 18 = 2 log 3 + log 2 -----Applying = b log a
log 18 = 2(.477) + .301 ------ Substituting given values of log 2 and log 3
log 18 = .954 + .301
log 18 =