How do you solve logx^3=3?

Answer 1

GIVEN:
LOG (x³) = 3
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FIND:
The value of "x".
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REMEMBER:
We can not take the LOG of values for "x" that are ≤ 0.
This will produce a statement where x is UNDEFINED.

THEREFORE:
x³ > 0
³√(x³) > ± ³√(0)
x > ± (0)
x > ± 1(0)
x > 0
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SOLUTION:
LOG (x³) = 3 ; x > 0

If the quantity that we are taking the LOG of is raised by an EXPONENT. . .

We can move that EXPONENT to the front of the LOG and MULTIPLY the LOG by that EXPONENT.
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LOG (x³) = 3
3LOG (x) = 3

Next, DIVIDE "both" sides by 3 to isolate LOG (x) on the LHS.
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3LOG (x) = 3
[3LOG (x)] / 3 = 3 / 3

REDUCE.
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[3LOG (x)] / 3 = 3 / 3
LOG (x) = 1

Now, let's change this equation from LOG FORM into BASE FORM.
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LOG FORM:
LOG (with a base)_(the quantity taking the LOG of) = the EXPONENT

EXPONENT FORM:
(base)^(the EXPONENT) = the quantity that we're taking the LOG of
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REMEMBER:
If there is no base written, the base = 10
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LOG (x) = 1
LOG(with a base of 10)_(x) = 1

(base)^(the EXPONENT) = the quantity that we're taking the LOG of
(10)^(1) = x

SIMPLIFYING the EXPONENTS we get. . .
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10 = x ; x > 0

CHECK to make sure that "x" is not a RESTRICTED value.
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RESTRICTION CHECK:
10 = x ; x > 0
10 > 0 is a TRUE statement.
Therefore, x = 10 could be a solution to the equation.

CHECK with the ORIGINAL EQUATION by SUBSTITUTING for "x".
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LET:
x = 10

SUBSTITUTION CHECK:
LOG (x³) = 3
LOG [(10)³] = 3
LOG (1,000) = 3
LOG (with a base of 10)_(1,000) = 3

CHANGE to EXPONETIAL FORM.
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LOG (with a base of 10)_(1,000) = 3

EXPONENTIAL FORM:
(base)^(the EXPONENT) = the quantity that we're taking the LOG of

(10)^3 = 1,000
1,000 = 1,000 is a TRUE statement.
Therefore, x = 10.

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FINAL ANSWER:
x = 10 ; x > 0

GREAT question! ♥
Thanx for keep'n my skills up! :o)

Answer 2

It is 10.

Answer 3

log x^3=3
3*log x=3
log x = 1

x = 10

₢

Answer 4

log (x^3)=3
3*log (x)=3
log x = 1
x=10^1
x=10

Answer 5

log(x^3)=3
3 log(x) = 3
log(x) = 1
10^(log(x)) = 10^1
x = 10

Answer 6

log(x^3) = 3
3log(x) = 3
log(x) = 1
x = 10

Answer 7

assuming that log base 10
then
10 ^ 3 = x ^ 3
so x=10