Help with Algebra problems?

Question

Okay it says Use Log3(small 3 at the bottom of Log) 2= 0.6310 and Log3(small 3 at the bottom of Log) 7 = 1.7712 to evaluate each expression. I have a few questions. The first one says Log3 7/2. Another problem is Log3 18. Another problem is Log3 2 + log3 7 = log3x. Then it says log5 42 - log5 6 = log5 k. Then it says log10 y= 1/4 log10 16 + 1/2 log10 49. Remember the numbers that is next to the word log is like small and at the bottom of the word Log. I don't know what they mean. Please help me out with these problems if you can.

Answer 1

log(3)2 = .6310
log(3)7 = 1.7712

log(3)(7/2)
log(3)7 - log(3)2
1.7712 - .6310
1.1402

log(3)(7/2) = 1.1402

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log(3)(18) =
log(3)(9 * 2) =
log(3)(9) + log(3)2 =
log(3)(3^2) + log(3)2 =
2log(3)3 + log(3)2 =
2(log(3)/log(3)) + log(3)2 =
2 + log(3)2 =
2 + .6310 =
2.631

log(3)18 = 2.631

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log(3)2 + log(3)7 = log(3)x
log(3)(2 * 7) = log(3)x
log(3)14 = log(3)x
x = 14

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log(5)(42) - log(5)6 = log(5)k
log(5)(42/6) = log(5)k
log(5)7 = log(5)k
k = 7

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log(10)y = (1/4)log(10)16 + (1/2)log(10)(49)
log(10)y = log(10)(16^(1/4)) + log(10)(49^(1/2))
log(10)y = log(10)(2) + log(10)(7)
log(10)y = log(10)(2 * 7)
log(10)y = log(10)14
y = 14

Answer 2

While the common bases for logarithms is base 10 and base (e), which is often called Natural logarithms, in theory any base can be used. The logarithmic values are different between bases, but the logarithmic operations are the same.

Here, we have base 3 logs. As a yardstick, log3 of 3 is 1, log3 of 9 is 2, etc., if you get my drift.
So if you have log3 of 7/2, this is same as
log3 7 - log3 2 = log3 (3.5).

In the problem log3 2 + log3 7 = log3 x, we are doing the log operation analogous to 2x7. The log sum will be the log3 of 14, so x= 14.

This should help you out.

Answer 3

The problem info is as follows"

Log base 3 of 2 = 0.6310 ( 3^0.6310) = 2
or 3 raised to the 0.6310 power = 2
Log base 3 of 7 = 1.7712

When you work with logs, you treat the log of a number as an exponent because that'
essentially what it is.

Rule 1: When you multiply with exponents, you add the exponents.

Rule 2: When you divide with exponets you sutract the exponents.

Thefefore, by Rule 2,

Log base 3 of 7/2 = 1.7712 - 0.6310
= 1.1402

Use this process and the rules to figure out the rest of the problelms. You can't learn if someone else does the work.

It's the same principle that you use for base 10 problems which is our everyday numbering system. A simple example might help:
Log base 10 of 10 = 1, (10^1 = 10)
Log base 10 of 100 = 2, (10^2= 100)

So, log base 10 of 100 / log base 10 of 10
which = 2 -1 = 1 which equates to 10^1 = 10
Or 100/10 = 10!

Answer 4

u can only put log base 10 in calculator study hard alg2 is a killer to the brain

Answer 5

hi chum this a normal question consistent with linear equations you need to use transposition technique in this methodology whilst a term is transfered from one side to different its sign turns into opposite answer: x+4-7x=22 =4-7x=22-x (right here x comes from the left side its sign ameliorations) =4=22-x+7x(right here 7x comes from the left side its sign ameliorations) =4-22=6x(comparable) =-18=6x x=-18/6 =-3 Bye Bye!!!!!!!!!!!!!!!!!!!!!!