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# 1/2 Log r + 1/3 log s - 1/4 log t

I don't understand the question at all...

L = 1/2 log r + 1/3 log s - 1/4 log t

Use Power Rule of Logarithms:

L = log(r^(1/2)) + log(s^(1/3)) - log(t^(1/4))

Use Multiplication Rule of Logarithms:

L = log( (r^(1/2)) * (s^(1/3)) ) - log(t^(1/4))

Use Quotient Rule of Logarithms:

L = log( ( (r^(1/2)) * (s^(1/3)) ) / (t^(1/4)) )
The question is combine all log terms as one log

We make use of properties of log function:

log AB = log A + lobB

A = ab      b = log aA

1/2 log r + 1/3 logS - 1/4 log t

log (√r . 3√s) / 4√t ) = log 24√( r12 . S8/  t6 )

Note that    a1/n n√a

n√a . m√b  = mn√ (an . bm )
Hi Juan;
I do not know what you are trying to do.  I will do my best...
1/2 Log r + 1/3 log s - 1/4 log t
Let's apply the principle of...
log xy=y log x
log r1/2+log s1/3-log t1/4
Let's apply the principle of...
log ab=log a + log b
log (r1/2)(s1/3)-log t1/4
Let's apply the principle of...
log a/b=log a - log b
log[(r1/2)(s1/3)]/(t1/4)