What would log3 =

Question

20•log3(11y)=log 3 ( )

Answer 1

20log₃(11y) = log₃(11y)²⁰

Answer 2

20log(11y) base 3

= 20log11 + 20logy base 3

= log(11^20) + log(y^20) base 3

= about log(6.72749995 x 10^20) + log(y^20) base 3

or

= log(11y)^20) base 3 (some people stop here, or you can go further)

= about log(6.72749995y x 10^20) base 3

=about log6.72749995) + log(10^20) base 3

= about log6.72749995 + log200,000,000,000,000,000,000 base 3

= log(200 quintillion) + about log6.272749995 base 3

= log(

Answer 3

The way the question is asked implies that the "3" is the base of the logarithm, in which case it should appear as a subscript.

20log₃(11y)=log₃(11y)²⁰

But why?

A logarithm is an exponent of a base

8=2³. Therefore, Log₂8=3

To write "Log₂8=3" is to say that 3 is the exponent (Log) of 2 (the base) that results in 8 when the base is raised to that exponent.

Because a logarithm is an exponent, they follow the rules of exponents.

b^mbⁿ=b^m+n

And when R is written as b raised to some exponent, m, such that R=b^m and Log_bR=Log_bb^m=m

and T is written as b raised to some exponent, n, such that T=bⁿ and Log_bT=Log_bbⁿ=n

Log_bRT=Log_bb^mbⁿ =Log_bb^m+n=m+n=Log_bR+Log_bT

(b^m)ⁿ=b^mn

And because Log_bb^m=m,

Then if we express R as b raised to some exponent, m, such that R=b^m,

Log_bRⁿ=Log_b(b^m)ⁿ=Log_bb^mn=mn=nm=nLog_bb^m=nLog_bR

Answer 4

The question is log 3 = x and we have to find x. Lots of ways to do it. One easy way is to remind ourselves that another way of putting the question is "what power is base 10 raised to to give us a three?" In terms of equations we could plot y = 3 and y = 10 ^x on our calculators and see where they intersect. I did it and got x = 0.477 rounded to three places. Makes sense as 10 ^1 -= 10, so the answer for x must be less than 1 in order to get 3.