logx(3) = log10(7)
(assumed the common logarithm (base 10) for "log7")
x^(logx(3)) = x^(log10(7))
3 = x^(log10(7))
log10(3) = log10(x^(log10(7)))
log10(3) = log10(7)log10(x)
(log10(3)/log10(7)) = log10(x)
10^(log10(3)/log10(7)) = x
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log7(117) = 2.447273291
log(f) + log(0.1) = 6 So log(f*0.1) = 6 so f*0.1 = 106 so f = 107
Use the identity log(ab) = log a + log b to combine the logarithms on the left side into a single term. Then take antilogarithms (just take the log away) on both sides.
When solving this problem:1/2log7x = log720 - 2(log72 + log75)There are two things to note:lognx + logny = logn(xy)a(lognx) = lognxaUsing those two rules, we can simplify the given expression:1/2log7x = log720 - 2(log72 + log75)log7x1/2 = log720 - 2(log710)log7x1/2 = log720 - log7102log7x1/2 = log720 - log7100log7x1/2 = log7(1/5)√x = 1/5x = 1/25
log x + 2 = log 9 log x - log 9 = -2 log (x/9) = -2 x/9 = 10^(-2) x/9 = 1/10^2 x/9 = 1/100 x= 9/100 x=.09