Solve the following equation for x: (logx)^3 = log x^3?

Question

Choose between the following answers
(a) x = 1 or x = 0.0185
(b) x = 0 or x = 2.2
(c) x = 2, x = 23.4 and x = 0.0185
(d) x= 1, x = 53.95 and x = 0.0185

Answer 1

First, simplify the equation.

log(x^3) = 3log(x), so

(log(x))^3 = 3log(x), so

(log(x))^3 - 3log(x) = 0, now factor the left side as

log(x)((log(x))^2 - 3) = 0, now this is true whenever log(x) = 0 or ((log(x))^2 - 3) = 0

log(x) = 0 whenever x = 1, so answers (b) and (c) are eliminated right away.

((log(x))^2 - 3) = 0 means that ((log(x))^2 = 3 so that

log(x) = +sqrt(3) or -sqrt(3), i.e. there are two solutions. This means that there are 3 solutions all together, so (a) is eliminated. That leaves (d).

In fact, log(x) = +sqrt(3) means that x = 10^sqrt(3) which is about 53.95, and x = 10^(-sqrt(3)) which is about 0.0185.

HTH

Charles

Answer 2

Well, this is pretty simple

lets start off by stating :

d/dx ln x = e^x+C

Then log x ^3 = 3 log x /3 log 10

For x of all x in the elements of the real

d /dx log x = 10^x+ C

10^(o) = 1

therefore x has to be 1and 53.95, and 0.0185

Answer 3

(logx)^3 = log x^3

(logx)^3-3logx=0

logx( (logx)^2 - 3) = 0

hence, logx = 0 ==> x=1 [ solution 1 ]
or
(logx)^2 = 3
logx = ± 1.7320508075688772935274463415059
x = antilog( ± 1.7320508075688772935274463415059)
x = 53.9573742880834 [solution 2] or x = 0.018533148260488945 [ soultion 3]

hence the answer is (d) x= 1, x = 53.95 and x = 0.0185

Answer 4

Given: log (x^2) + log (x+3) - log (x) =1 Recall: log a + log b = log (ab) Recall: log c - log d = log (c/d) So, log {[(x^2)*(x+3)]} / (x) = 1 log [(x^3 + 3x^2)] / (x) = 1 log (x^2 + 3x) = 1 Don't know how I have gotten log (x^2 + 3x)? It's easy; x^3/x is the same as x^(3 - 1) = x^2. And, 3x^2/x is the same as 3x^(2) - (1) = 3x. Got it? :) Now, log (x^2 + 3x) = 1 Log has a base of 10. Recall that log a = b is the same as a = 10^b (x^2 + 3x) = 10^1 (x^2 + 3x) = 10 x^2 + 3x - 10 = 0 (x + 5) (x - 2) = 0 x + 5 = 0 x = -5 (rejected cos it's negative) x - 2 = 0 x = 2 So, answer is x = 2.

Answer 5

(logx)^3 = log x^3
(logx)^3 = 3log x
(logx)^2 = 3
log x =+/- sqrt(3)
10^logx =10 ^(+/- sqrt(3))
x = 10^(sqrt(3) or 10^(-sqrt(3)
x = 53.95 or x = 0.0185

Answer 6

(logx)^3 = log x^3
(logx)^3 - log x^3 = 0
(logx)^3 - 3log x = 0
(logx) ((logx)^2 - 3) =0
(logx) (logx +3^0.5) (logx - 3^0.5) =0

logx = 0
x=1

logx + sqrt(3) = 0
logx = -sqrt(3)
x = 0.0185

logx - sqrt(3) = 0
logx = sqrt(3)
x = 53.95

so, the answer is (d)

Answer 7

you are so clever that you put your homework on the Internet and you are so foolish that you can not work it out.
the answer is D

Answer 8

are you asking us to do your homework?