If `4^44 + 4^44 + 4^44 + 4^44 = 4^x` , then x equals:
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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.
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` .
Can anyone plz solve it by using logarithm.....
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