X= log base 3 1/27
27 = x ^ -3
3 ^ 3 = 1 / (x^3) {factorise 27 and invert x^-3}
ln(3 ^3) = ln( 1 / (x^3) ) { ln both sides}
ln(3^3) = ln(1) - ln(x^3) {apply the log rule for division}
3ln(3) = 0 - 3ln(x) {ln(1) = 0 in all bases}
ln(3) = -ln(x)
-ln(3) = ln(x) {multiple both sides by -1}
ln(3 ^ -1) = ln(x) {bring the minus one back inside the log term}
3 ^ -1 = x {raising 3 to the power of -1 is 1/3}
1/3 = x
log(base x) 27 = -3
x^-3 = 27
x^-3 = 3^3
1/x^3 = 3^3
1 = (3^3)(x^3)
x^3 = 1/3^3
x^3 = 1/27
x = 1/3 answer
either one
That's a lot of work
since 3^3 = 27,
3^-3 = 1/27
so, log_3(1/27) is thus -3
Why did 1/27 go to therapy?
Because it had a negative self-log-esteem!
Anyway, let's solve your equation. Since we have x = log₃(1/27), we can rewrite 1/27 as 3⁻³, which means x = log₃(3⁻³).
Now, let's use the property of logarithms that says logₐ(a^b) = b to simplify further. Since we have log₃(3⁻³), we can rewrite it as -³.
Therefore, x = -³, which means x equals -3.
To evaluate the expression X = log base 3 (1/27), we can use the properties of logarithms to simplify it.
Since the base of the logarithm is 3, we can rewrite 1/27 as a power of 3:
1/27 = 3^(-3)
Now, we can rewrite the expression as:
X = log base 3 (3^(-3))
According to the logarithm property, log base b (b^x) = x. So, we can simplify further:
X = -3
Therefore, the value of X is -3.
To find the value of x in the equation x = log base 3 (1/27), we need to understand the properties of logarithms.
A logarithm is the exponent to which the base must be raised to obtain a certain number. In this case, we have the logarithm base 3 of 1/27. The question is asking, "What power must we raise 3 to obtain 1/27?"
To solve this equation, we can rewrite 1/27 as a power of 3. Since 3^3 equals 27, we can express 1/27 as (1/3)^3. Therefore, we can rewrite the original equation as x = log base 3 [(1/3)^3].
Applying the exponent rule for logarithms, we can move the power as a coefficient in front of the logarithm. Doing so, we get x = 3 * log base 3 (1/3).
The next step is to simplify the logarithm expression inside. In logarithms with the same base, we can rewrite it as an exponent. Therefore, log base 3 (1/3) can be expressed as 3^(-1) (since 3 raised to the power of -1 gives 1/3).
Substituting this simplification back into the equation, we have x = 3 * 3^(-1).
To simplify further, we multiply 3 by 3^(-1), which gives us x = 3 * (1/3).
Finally, multiplying 3 by 1/3, we find that x = 1.
Therefore, the value of x in the equation x = log base 3 (1/27) is 1.