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Answers by Maurizio T.

log1/4[(1/4)-2x] = log1/4(64)  -2x = log1/4 64 -2x = log10(64)/log10(1/4) = loge(64)/loge(1/4) = -3 Thus x = 3/2 = 1.5   In fact we can check that (1/4)-2(3/2) = (1/4)-3 = 43 = 64   Remember that to find logaB for any base a, we can always use the logs...

log(log x)=4 (answer)

Well... 10,000 cannot be right. In fact,   log(log(10,000) = log(4) .   Think of it like this:   10log(log(x)) = 104   which is the same as:   log(x) = 104   And therefore x = 10^104 which is a huge number:  1010...

Math problem (answer)

If you use log() for logarithm in base 10, then from   log(x+3) = 3   to pass to an exponential form we do the following:   10log(x+3) = 103 = 1000   (*).   Now, using properties of log's, it follows that   10log(x+3)...

Call A the slower car and B the faster car. Let x be the speed of B Then, according to the text of the problem, the speed of A is x-10. Since the cars are traveling toward each other, when they meet the sum of the distances each car has traveled is 400. So, the problem can be solved...

This topic deals with implicit differentiation for which I am sure your textbook has a lot to say. I assume that you are expected to find y'(x) = dy/dx since nothing is specified in the text of the problem and that is usually what is done, i.e., we are working as if y=y(x).   Look...

To find the domain of the function assigned, the natural log, you need to specify for which values of x, the function is well defined. We know that for logarithms in general, natural or in any base, we need the argument to be positive, i.e.,   x^2 - 3x - 4 > 0   Now...

Variables are  m = number of cars; n = number of buses;   max: Profit = 2.50*m +7.50*n   s.t.:  6*m+30*n <= 600  (we can use 60% of the total 20x50=1000 sqm parking lot)         n+m <= 60      ...

The easiest, and perhaps the only way, to solve this kind of problems is to write   y = g(x) = x+1     and solve this equation as a function of y, i.e.,  x = y-1.   Therefore, the inverse function you are looking for is given by g-1(x) = x-1...

Let x be the number of rows.   Leo plants x+29 trees in each row.   Hence the number of rows is given by   912            x ------  =   x+29   i.e., after simple algebraic manipulations,   912=...