write the equations in logarithmic form.
1. 216 =6^3
2. 25 =(1/5)^-2
3. a = b^c
log6216 = 3
log1/525 = -2
logba = c
To write the given equations in logarithmic form, we need to understand the relationship between exponentiation and logarithms.
In logarithmic form, the equation will have the logarithm of the base on one side, followed by the result of the exponentiation operation on the other side.
Let's rewrite the equations in logarithmic form:
1. To write 216 = 6^3 in logarithmic form, we need to determine the logarithm base. Assuming the base is 6, we get:
log(base 6) 216 = 3
2. For 25 = (1/5)^-2, the base is (1/5). We can write it as:
log(base 1/5) 25 = -2
3. Finally, the equation a = b^c can be written as:
log(base b) a = c
These logarithmic forms express the relationship between exponentiation and logarithms, where the logarithm of a number to a particular base allows us to find the exponent that produces that number.