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If `4^44 + 4^44 + 4^44 + 4^44 = 4^x` , then x equals:a.45b.203c.4444d.44444
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High School Teacher
Since 4^44 is added four times by itself, left side can be express as:
To simplify the left side further, apply the properties of exponent when multiplying same base which is `a^m*a^n=a^(m+n)` .
Since both sides of the equation has same base, to solve for x, set the exponents of each side equal to each other.
Posted by mjripalda on March 3, 2013 at 10:55 AM (Answer #1)
One important logarithmic property that can be used to solve this:
`log x^a = a*log x`
Taking the log of both sides:
`log (4^44+4^44+4^44+4^44) = log (4^x)`
`=> log (4^44+4^44+4^44+4^44) = x* log (4)`
`=> (log(4^44+4^44+4^44+4^44))/(log(4)) = x`
As explained in the other answer, the sum of 4 to the 44th power equals 4 to the 45th power.
`=> (log (4^45))/(log(4)) = x`
`(45*log(4))/(log(4)) = x`
The logs cancel out. Therefore `45=x` .
Posted by Wilson2014 on March 6, 2013 at 11:33 PM (Answer #3)
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