SOLUTION: How do I simplify:
4^{log [2^(log 5)]}
*both logs have a base of 2*
Thanks
Algebra.Com
Question 189102: How do I simplify:
4^{log [2^(log 5)]}
*both logs have a base of 2*
Thanks
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Remember, }=x)
is one identity that is useful for simplifying logarithms.
So }=5)
(in this case, and )
This means that
}\right)})
simplifies to
})
In other words, }\right)}=4^{\log_{2}\left(5\right)})
-----------------------------------------------------------------
Now let's simplify
^{\log_{2}\left(5\right)})
... Rewrite as
^{2\log_{2}\left(5\right)})
... Multiply the exponents.
^{\log_{2}\left(5^2\right)})
... Rewrite the inner log using the identity
^{\log_{2}\left(25\right)})
... Square 5 to get 25
... Use the first identity given to simplify
So }=25)
===========================================================
Answer:
This means that }\right)}=25)
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