While solving any log based question, it is always advisable to reduce the expression such that all (or most) of the numbers involved in it are prime numbers. As in this case, we can reduce log_a81 to some form of log_a3.Recalling an important property of log, which is: log_ab^c = c*log_ab we see that 81 can be written as 3^4 . Now using the above mentioned property, we can write log_a81 as 4*log_a3 .
:. log_a81 = log_a3^4
:. log_a81 = 4*log_a3
:. log_a81 = 4*1.618
:. log_a81 = 6.472
To answer this question, use the following rule of logarithms:
log_a x^b = blog_a x
This means that logarithm of any base of a number taken to the power b equals b multiplied by the logarithm of the same base of that number.
In this case, the number is 3, and the logarithm of the base a of 3 is given: log_a 3 = 1.618
The number 81 is a power of 3:
3^4 = 81
So, the logarithm of base a of 81 can be rewritten, using the above rule, as
log_a 81 = log_a 3^4 = 4log_a 3
and calculated as 4(1.618) = 6.472.
Therefore, the value of
log_a 81
is 6.472.
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