Express (In 35+ln(1/7))/ In 25 in terms of In 5 and In 7

Properties of the logarithm: for any base of logarithm,

log(a*b) = log(a) + log(b)

If we replace b with 1/b, or b^-1, we have

log(a/b) = log(a) + log(1/b) = log(a) - log(b)

since

log(1/b) = log(b^-1) = - log(b)

using the power property of logarithms,

log(b^n) = n log(b)

Now,

ln35 = ln(5*7) = ln5 + ln7

ln(1/7) = - ln7

ln25 = ln(5^2) = 2 ln5

Putting everything together, we have

(ln35 + ln(1/7))/ln25 = (ln5 + ln7 - ln7)/(2 ln5) = ln5/(2 ln5) = 1/2

answer: the value of x is 7cm

step-by-step explanation:

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752