How do you simplify log(2square root of 10)-1/3 log0.8-log10/3
Log[2sqrt(10)] -(1/3)Log(0.8) -Log(10/3) -------(i)Originally Posted by kingkaisai2
Is that what you mean?
If yes, do you want to combine the 3 logs into one log only?
If yes again, then,
= Log[2sqrt(10)] -Log[cubrt(0.8)] - Log(10/3)
= Log{[2sqrt(10)] / [cubrt(0.8)] / (10/3)} ----------(ii)
Umm, it's getting too complicated. Let us simplify the 3 logs separately, for simplicity.
I assume, by "simplify", you mean no decimal points.
Log[2sqrt(10)]
= Log[2*(10)^(1/2)]
= Log(2) +Log(10^1/2)
= Log(2) +(1/2)Log(10)
= Log(2) +(1/2)(1)
= Log(2) +(1/2) ------**
(1/3)Log(0.8)
= (1/3)Log[8/10]
= (1/3)[Log(8) -Log(10)]
= (1/3)Log(8) -(1/3)Log(10)
= (1/3)Log(2^3) -(1/3)(1)
= Log[(2^3)^(1/3)] -(1/3)
= Log[2] -(1/3) ----------**
Log(10/3)
= Log(10) -Log(3)
= 1 -Log(3) ----------------**
Therefore, (i) becomes
= [Log(2) +(1/2)] -[Log(2) -(1/3)] -[1 -Log(3)]
= 1/2 +1/3 -1 +Log(3)
= (3 +2 -6)/6 +Log(3)
= -1/6 +Log(3)
= Log(3) -(1/6) ----------------------------answer.
Check,
Using a calculator,
Log[2sqrt(10)] -(1/3)Log(0.8) -Log(10/3)
= 0.80103 -(-0.03230) -0.52288
= 0.31045
Log(3) -1/6
= 0.47712 -0.16667
= 0.31045
They are the same, so, OK.
Hello, kingkaisai2!
I assume I'm reading it correctly . . .
We have:Simplify:
Then:
And:
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
If you really want to impress/surprise/terrify your teacher, keep going.
The denominator is:
. . .
The fraction becomes:
Rationalize: