Well, well, well, look who's trying to flex their math muscles! Differentiating 3 log x is as easy as pie. The derivative of 3 log x is simply 3/x. So, there you have it, darling, short and sweet, just like me.
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*First off if we assume this log to be base 10
next we can use the product rule (d/dx (3)*logx+d/dx(logx)*3)
1.derivative of a constant is zero
so that gives us 0*logx as our first term (simplifies to zero)
next we have to differentiate logx
that gives us 3*(1/xln(10))
so that leaves 0logx+3*(1/xln(10))
simplify...... 3/xln(10)
Log (x^3) = 3 log(x) Log of x to the third power is three times log of x.
1
If the log of x equals -3 then x = 10-3 or 0.001or 1/1000.
x = 3*log8 = log(83) = log(512) = 2.7093 (approx)
log(9x) + log(x) = 4log(10)log(9) + log(x) + log(x) = 4log(10)2log(x) = 4log(10) - log(9)log(x2) = log(104) - log(9)log(x2) = log(104/9)x2 = 104/9x = 102/3x = 33 and 1/3