log5 +log2 =log(5x2)=log(10)=log10(10)=1
log5(2) + log5(10) - log5(4) = log5(20/4) = log5(5) = 1
log5 20 + log5 10 - 3log5 2 = log5 [(20*10)/(2^3)] = log5 25 = 2 (log5 5) = 2
log1 + log2 + log3 = log(1*2*3) = log6
1.268293446
The browser which is used for posting questions is almost totally useless for mathematical questions since it blocks most symbols.I am assuming that your question is about log base 3 of (x plus 1) plus log base 2 of (x-1).{log[(x + 1)^log2} + {log[(x - 1)^log3}/log(3^log2) where all the logs are to the same base - whichever you want. The denominator can also be written as log(3^log2)This can be simplified (?) to log{[(x + 1)^log2*(x - 1)^log3}/log(3^log2).As mentioned above, the expression can be to any base and so the expression becomesin base 2: log{[(x + 1)*(x - 1)^log3}/log(3) andin base 3: log{[(x + 1)^log2*(x - 1)}/log(2)
i believe it is 7lnx, but don't quote me on it.
Original problem: log2(y-4) + log2y = 2The first step is applying a log property to the first term which states that logbn + logba = logb(na)So we can change the left side of the equation to log2[y(y-4)] or log2(y2-4y).Then we apply another log property which states logbn = a is equivalent to ba = nSo we can change log2(y2-4y) = 2 to the equation 22 = y2-4yor 4 = y2 - 4yNow we can swing the four around to make the quadratic y2 - 4y - 4 = 0Unfortunately, whoever assigned you this problem decided to make it more difficult because the expression y2 - 4y - 4 is unfactorable, meaning you have to use the quadratic formula. With it, you should be able to find the two values for y: 2 ± √32/2
3 dB is a change in power by a factor of 2. If it is plus, i.e. +3dB, power is doubled. If it is minus, i.e. -3dB, power is halved. 6 dB, then is a factor of four, or quarter; 6 dB is a factor of eight, or eighth, etc. The actual equation is 3 log2 (POWER OUT / POWER IN).
You use the identities: log(ab) = b log(a), and log(ab) = log a + log b. In this case, 5 log42 + 7 log4x + 4 log4y = log432 + log4x7 + log4y4 = log4 (32x7y4).
assuming the bases are the same, you can factor the log out, so you get:x^2 = 2 + 3x-4 (note that 2logx can be rewritten as logx^2 )x^2 - 3x +2 = 0You can factor this out: (x-1)(x-2) = 0so x must be one or x is two --> X=1 V X=2
76 plus 54 plus 92 plus 88 plus 76 plus 88 plus 75 plus 93 plus 92 plus 68 plus 88 plus 76 plus 76 plus 88 plus 80 plus 70 plus 88plus 72 equal 1,440
The answer is 672.