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]
Example 27=n3 : Take the cube root of 27. In general find the log, divide it by the power, then take the antilog.
11011 base 2 is equal to 27 in base 10 321 base 4 is equal to 57 in base 10 27+57=84
log(x) + 4 - log(6) = 1 so log(x) + 4 + log(1/6) = 1 Take exponents to the base 10 and remember that 10log(x) = x: x * 104 * 1/6 = 10 x = 6/1000 or 0.006
log37 - log3x = 4 log3(7/x) = 4 7/x = 34 = 81 x = 7/81
Log base 3 of 81 is equal to 4, because 3 ^ 4 = 81. Therefore, two times log base 3 of 81 is equal to 2 x 4 = 8.
The answer is 16
If log644 = x, then 64x = 4. The cubed root of 64 (which is the same as 641/3) is 4, so log base 64 of 4 is 1/3.
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]
log325 + log34 = log3(25*4) = log3(100) = log10100/log103 = 2/log103
log 100 base e = log 100 base 10 / log e base 10 log 100 base 10 = 10g 10^2 base 10 = 2 log 10 base 10 = 2 log e base 10 = 0.434294 (calculator) log 100 base e = 2/0.434294 = 4.605175
Example 27=n3 : Take the cube root of 27. In general find the log, divide it by the power, then take the antilog.
11011 base 2 is equal to 27 in base 10 321 base 4 is equal to 57 in base 10 27+57=84
9x = 27 log(9) + log(x) = log(27) log(x) = log(27) - log(9) log(x) = log(27/9) 10log(x) = 10log(27/9) x = 27/9 x = 3 This strikes us as the method by which the federal government might solve the given equation ... after appointing commissions to study the environmental impact and recommend a method of solution, of course.
log base 2 of [x/(x - 23)]
Be careful . On calculatoirs there are TWO logarithm bases, indicated by 'log' and 'ln'. They are not interchangeable. 'log' is logs to base '10' 'ln' is logs to the 'natural' base ; natural = 2.718281828.... Try 'log' , 'number'. '=' and the answer should appear. e.g. log(4) = 0.6020599999.... ln(4) = 1.386294371.... Note the two different answers. Notwithstanding, what is written above, by a special higher level mathemtics , log bases can be changed. However, whilst learning logarithms, keep to 'base 10' ( log).
The log of infinity, to any base, is infinity.