SOLUTION: please help me simplify these logarithms, I use {{{ log( b, N) = k }}} for logarithmic form ,{{{ log( 9, 1/27 ) }}} , {{{ log ( 9, sqrt( 3 ) )}}}, {{{ log ( 8, root( 3, 2 ))}}}, an

Question 742270: please help me simplify these logarithms, I use for logarithmic form , , , , and
Found 2 solutions by stanbon, lwsshak3:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
log( 9, 1/27 ) = log(1/27)/log(9) = -3/2
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log ( 9, sqrt( 3 ) ) = log(sqrt(3))/log(9) = (1/2)/2 = 1/4
-------------------------------------------------
log ( 8, root( 3, 2 )) =
log8(2^(1/3)) = log(2^(1/3))/log(2^3) = (1/3)/3 = 1/9
---------------------------------
log ( 3, root( 3, 1/9 ))}}}
log3[(1/9)^(1/3)] = log(1/9)^(1/3)/log(3) = (1/3)log(1/9)/log(3)
----
= (1/3)*(-2)/1 = -1/6
=============================
Cheers,
Stan H.
================
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
, , , , and
***
exponential form: base(b) raised to log of the number(k)=number(N)
using x in place of k
..

9^x=1/27
3^2^x=1/3^3
3^2x=3^-3
2x=-3
x=-3/2

..

9^x=3^(1/2)
3^2x=3^(1/2)
2x=1/2
x=1/4

..

8^x=2^(1/3)
2^3x=2^(1/3)
3x=1/3
x=1/9

..

3^x=(1/9)^(1/3)
3^x=(3^-2)^(1/3)
3^x=3^(-2/3)
x=-2/3

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