Convert to a logarithmic equation: 9y = 6561
You obviously meant to say
9^y = 6561
then
y = log9 6561
To convert the given equation, 9y = 6561, into a logarithmic form, we need to understand the relationship between logarithms and exponentiation.
In logarithms, we have a base, an exponent, and a result. The logarithm of a number to a specific base is the exponent needed to raise that base to reach the given number.
In this case, the base is unknown. To determine the base, we need to isolate y on one side of the equation. Let's divide both sides of the equation by 9:
(9y)/9 = 6561/9
Simplifying, we get:
y = 729
Now, we can rewrite the equation using logarithms. The logarithmic form for exponentiation is:
log(base)(result) = exponent
So, in this case, we have:
log(base)(729) = y
Note that we still haven't determined the specific base. To find the base, we can rely on the fact that 729 can be written as a power of a whole number. In this case, 729 is equal to 3^6. Therefore, we can rewrite the equation one more time:
log(3)(729) = y
Therefore, the logarithmic form of the equation 9y = 6561 is log(3)(729) = y.