If `4^44 + 4^44 + 4^44 + 4^44 = 4^x` , then x equals:a.45b.203c.4444d.44444
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` .
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.