the two things that you need to cut a log is a chain saw and sledge hammer.
6 minutes
-2
Due to the rubbish browser that we are compelled to use, it is not possible to use any super or subscripts so here goes, with things spelled out in detail: log to base 2a of 2b = log to base a of 2b/log to base a of 2a = [(log to base a of 2) + (log to base a of b)] / [(log to base a of 2) + (log to base a of a)] = [(log to base a of 2) + (log to base a of b)] / [(log to base a of 2) + 1]
log(x) + log(2) = log(2)Subtract log(2) from each side:log(x) = 0x = 100 = 1
log(2) + log(4) = log(2x)log(2 times 4) = log(2x)2 times 4 = 2 times 'x'x = 4
You will need 14 two's multiplied together to equal 16384. the answer to this can be found by log2(16384) = 14. Since most calculators don't have log base 2, you can do this: log(16384)/log(2) = 14. You can use the 'base 10' log or natural log [ln(16384)/ln(2) = 14]
Before we deal with the question of how strong he has to be, let's find outwhat the job involves.In order to cut one log into 4 pieces, he has to make 3 cuts. It doesn't makeany difference how long the original log is, or whether the pieces are equal ...Three cuts.One cut takes him 2 minutes. IF HE CAN keep going at that rate, 3 cuts willtake him 6 minutes.The strength he needs is whatever it takes to keep sawing for 6 minutes. If he'snot that strong, then the job takes longer, because he has to stop and rest.So his ability to finish the job doesn't depend on how strong the man is.But the length of time it will take him does. If he can hoist the saw andmake one complete cut in 2 minutes, but then he needs to rest for a week,then he would need more than 6 minutes to finish the job.
1
3^(-2x + 2) = 81? log(3^(-2x + 2)) = log(81) (-2x+2)log(3) = log(81) -2x = log(81)/log(3) - 2 x = (-1/2)(log(81)/log(3)) + 1
Oh, dude, squaring a log is like squaring anything else - you just multiply it by itself. So, if you square the log of a number, you're just raising that number to the power of the log base twice. It's not rocket science, just some basic algebraic manipulation. Hope that clears things up for you!
You need two computers in order to do that.
[log2 (x - 3)](log2 5) = 2log2 10 log2 (x - 3) = 2log2 10/log2 5 log2 (x - 3) = 2(log 10/log 2)/(log5/log 2) log2 (x - 3) = 2(log 10/log 5) log2 (x - 3) = 2(1/log 5) log2 (x - 3) = 2/log 5 x - 3 = 22/log x = 3 + 22/log 5