log₃(1/27)
The logarithm of a number is the power to which a base must be raised to obtain that number
The logarithm of a number is the power to which a base must be raised to obtain that number. In this case, we have log₃(1/27).
To find the solution, we need to ask ourselves, what power do we need to raise 3 to in order to obtain 1/27?
If we rewrite 1/27 as 3 raised to a negative power, we get 1/27 = 3^(-3).
Now, let’s solve for the power. We have:
log₃(1/27) = log₃(3^(-3))
By the logarithmic property, we can bring the exponent down as the coefficient:
log₃(1/27) = -3 * log₃(3)
Since log₃(3) represents the power to which 3 must be raised to obtain 3, it simplifies to 1.
Therefore, we get:
log₃(1/27) = -3 * 1
Simplifying further gives us the final solution:
log₃(1/27) = -3
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