You can calculate that on any scientific calculator - like the calculator on Windows (if you change the options, to display as a scientific calculator). Log base 4 of 27 is the same as log 27 / log 4. You can use logarithms in any base to calculate that - just use the same base for both logarithms.
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.