OMG logarithms?

Question

i cant seem to find a property of logarithms that fit this problem

(log x)^3 = log x^9

could you walk me through it please?

Answer 1

(logx)^3=9logx
dividing by log x
(logx)^2=9
log x=3
x=10^3=1000 if the base is 10
otherwise e^3 if the base is e

Answer 2

Something's not right! Say you're using base 10 and x = 100

then log 100 = 2
2^3 = 8

now, for the right side:
100^9 = (10^2)^9 = 10^18
log 10^18 = 18

Something is wrong with what you've written.

Answer 3

(log x)^3 = log x^9
(log x)^3 = 9log x
let u = log x, then
u^3 = 9u
u^2 = 9
u = ±3
log(x) = ±3
x = e^3, 1/e^3, or
x = 10^3, 1/10^3
depending on which base you are using.

Answer 4

(logx)^3=9logx

let a be logx
a^3=9a
a^3-9a=0
a(a^2-9)=0
a(a+3)(a-3)=0
a=0 or a= -3 or a = 3

find the value of log x

a=0
log x = 0
x=1

a=3
log x = 3
x = 1000

a = -3
logx=-3
x = 1/1000

so the answer is:
x=1 or x = 1000 or x = 1/1000

hope i'm not wrong

Answer 5

(log x)^3 = log x^9
(log x)^3 = 9log x
(log x)^3 - 9log x = 0
log x [(log x)^2 - 9] = 0

Therefore,
log x = 0, => x = 1; or
(log x)^2 -9 = 0,
=> log x = +/-3
=> x = 0.001, 1000

Answer 6

what u write is wrong
why?
try subsituing.....

put x=100

then RHS=8
LHS=2*9=18

it seems to be wrong