If ln a=2, ln b=3, and ln c=5, evaluate the following:

(a) ln(a^−2/b^4c^−3)=
-.9524
(b) ln(√b^−4*c^1*a^−1)=
-1.739
(c) ln(a^2b^4)/ln(bc)^−2=
42.39
(d) (ln(c^−1))*(ln(a/b^3))^−4=
-.03507
I am getting these answers but the problem gives me an error saying "at least ONE of my answers is incorrect"
I'm not sure how as I used the (ln) rules and broke it apart several times and even plugged it into my calculator and I am getting the same results.

can someone help me or point out what i am doing wrong.
rules:
log(ab)= log a +log b
log (a/b) = log a - log b
log a^b = b log a

I think u are getting it wrong

Let's go through each calculation step-by-step and see if there's any mistake:

(a) ln(a^−2/b^4c^−3)
Using the logarithm rules:
ln(a^−2/b^4c^−3) = ln(a^−2) - ln(b^4c^−3)

Substituting the given values:
ln(a^−2/b^4c^−3) = ln(e^−4) - (ln(e^3) + ln(e^5))

Applying the rule ln(e^x) = x:
ln(a^−2/b^4c^−3) = -4 - (3 + 5)
ln(a^−2/b^4c^−3) = -12

The correct value is -12.

(b) ln(√b^−4*c^1*a^−1)
Using the logarithm rules and the square root rule:
ln(√b^−4*c^1*a^−1) = ln(b^(-4/2)) + ln(c^1) + ln(a^(-1))

Simplifying the exponents:
ln(√b^−4*c^1*a^−1) = ln(b^(-2)) + ln(c) + ln(a^(-1))

Applying the rule ln(a^x) = x ln(a):
ln(√b^−4*c^1*a^−1) = -2 ln(b) + ln(c) - ln(a)

Substituting the given values:
ln(√b^−4*c^1*a^−1) = -2 ln(e^3) + ln(e^5) - ln(e^2)
ln(√b^−4*c^1*a^−1) = -6 + 5 - 2
ln(√b^−4*c^1*a^−1) = -3

The correct value is -3.

(c) ln(a^2b^4)/ln(bc)^−2
Using the logarithm rules:
ln(a^2b^4)/ln(bc)^−2 = (ln(a^2) + ln(b^4)) / (ln(bc)^−2)

Simplifying the exponents:
ln(a^2b^4)/ln(bc)^−2 = (2 ln(a) + 4 ln(b)) / ((−2) ln(bc))

Substituting the given values:
ln(a^2b^4)/ln(bc)^−2 = (2 ln(e^2) + 4 ln(e^3)) / ((−2) (ln(e^3) + ln(e^5)))

Applying the rule ln(e^x) = x:
ln(a^2b^4)/ln(bc)^−2 = (4 + 12) / ((−2) (3 + 5))
ln(a^2b^4)/ln(bc)^−2 = 16 / (−16)
ln(a^2b^4)/ln(bc)^−2 = -1

The correct value is -1.

(d) (ln(c^−1))*(ln(a/b^3))^−4
Using the logarithm rules:
(ln(c^−1))*(ln(a/b^3))^−4 = (ln((c^−1)^−4)) * (ln(a/b^3))^−4

Simplifying the exponents:
(ln(c^−1))*(ln(a/b^3))^−4 = (ln(c^4)) * (ln(a/b^3))^−4

Applying the rule ln(a^x) = x ln(a):
(ln(c^−1))*(ln(a/b^3))^−4 = 4 ln(c) * (ln(a/b^3))^−4

Substituting the given values:
(ln(c^−1))*(ln(a/b^3))^−4 = 4 ln(e^5) * (ln(e^2/e^12))^−4

Applying the rule ln(e^x) = x:
(ln(c^−1))*(ln(a/b^3))^−4 = 20 * (ln(1/e^10))^−4

Applying the rule ln(1/x) = -ln(x):
(ln(c^−1))*(ln(a/b^3))^−4 = 20 * (-ln(e^10))^−4

Applying the rule ln(e^x) = x:
(ln(c^−1))*(ln(a/b^3))^−4 = 20 * (-10)^−4
(ln(c^−1))*(ln(a/b^3))^−4 = 20 * 0.0001
(ln(c^−1))*(ln(a/b^3))^−4 = 0.002

The correct value is 0.002.

Based on the calculations above, all the answers are correct. If the problem gives you an error message, there might be some other issue. Double-check the format or requirements of the problem, or try re-entering your answers to see if the error persists.

Let's go through each part of the question and see if we can identify any errors:

(a) ln(a^−2/b^4c^−3)

Using the logarithm rules you provided, we can rewrite this as:
ln(a^−2) - ln(b^4) - ln(c^−3)

Using the rule log a^b = b log a:
-2 ln(a) - 4 ln(b) - (-3) ln(c)

Now, we substitute the given values:
-2(2) - 4(3) - (-3)(5)
-4 - 12 + 15
-1

So the correct evaluation should be ln(a^−2/b^4c^−3) = -1, not -0.9524. Therefore, your answer for part (a) is incorrect.

(b) ln(√b^−4*c^1*a^−1)

Following the same steps, we can rewrite this as:
ln(sqrt(b^−4)) + ln(c^1) - ln(a^−1)

Using the rule log a^b = b log a:
(1/2)ln(b^−4) + ln(c) - (-1)ln(a)

Now, substitute the given values:
(1/2)(-4ln(b)) + ln(c) - (-1)(2)
-2ln(b) + ln(c) + 2

In order to evaluate this expression, we need to know the values of b and c. Please provide those values, as it seems they were not given in the question.

(c) ln(a^2b^4)/ln(bc)^−2

Following the logarithm rules, we have:
2ln(a) + 4ln(b) - 2ln(bc)

Substituting the given values:
2(2) + 4(3) - 2(5)
4 + 12 - 10
6

So the correct evaluation should be ln(a^2b^4)/ln(bc)^−2 = 6, not 42.39. Therefore, your answer for part (c) is incorrect.

(d) (ln(c^−1))*(ln(a/b^3))^−4

Following the steps:
(ln(c^−1)) * (ln(a) - ln(b^3))^−4

Using the rule log a/b = log a - log b:
(ln(c^−1)) * (ln(a) - 3ln(b))^−4

Now substitute the given values:
ln(c^−1) * (2 - 3(3))^−4
ln(c^−1) * (-7)^−4

Again, to evaluate this expression, we need the value of c. Please provide the value of c, as it seems it was not given in the question.

In summary, there are errors in your answers for parts (a), (c), and (d) of the question. Please check your calculations and the given values to identify the discrepancies.

(a) ln[c^3 / (a^2 b^4)] = (5 * 3) - [(2 * 2) + (3 * 4)] = -1

(b) ln[c / (a b^2)] = 5 - [2 + (3 * 2)]

not sure how you are getting your results
... you shouldn't need a calculator
... just follow the rules carefully