SOLUTION: Q. Find the value of the expression
{{{ 2/ log( 4, (2000)^6 ) }}} + {{{ 3 / log( 5, (2000)^6 ) }}}
My attempt (I would be only writing a select few steps, missing the unnec
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Question 202615: Q. Find the value of the expression
+
My attempt (I would be only writing a select few steps, missing the unnececarry ones)
=
=
=
=
=
I'm confused as to how to procede now!
btw. The answer is 1/6......I just don't know how to get there!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression.
Let
Replace every instance of with "x". This isn't necessary, but I find this substitution simplifies things a bit.
Use the change of base formula.
Note: the change of base formula is
Multiply by the reciprocal of the lower fractions.
Multiply.
Combine the fractions.
Rewrite each log using the identity
Square 4 to get 16 and cube 5 to get 125. note: (not 625)
Combine the logs using the identity
Multiply
Plug in
Rewrite the bottom log using the identity
Highlight the common terms.
Cancel out the common terms.
Simplify
So
You can verify this with a calculator.
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