How do you convert logarithmic form to exponential form?
To convert logarithmic form to exponential form, you need to remember the basic definitions of logarithms and exponentials.
Logarithmic form: log_b(x) = y
Exponential form: b^y = x
Here are the steps to convert logarithmic form to exponential form:
1. Identify the base (b) of the logarithm.
2. In the exponential form, the base (b) will be the same as the base in the logarithmic form.
3. The exponent (y) in the exponential form will be the same as the value on the right side of the equation in the logarithmic form.
4. The value (x) on the left side of the equation in the exponential form will be the same as the number inside the logarithm in the logarithmic form.
Example:
Logarithmic form: log_2(8) = 3
To convert this to exponential form:
1. The base is 2.
2. The exponential form will be 2^y = x.
3. The exponent will be 3.
4. The value will be 8.
So, the exponential form is: 2^3 = 8.
Another example:
Logarithmic form: log_5(25) = 2
To convert this to exponential form:
1. The base is 5.
2. The exponential form will be 5^y = x.
3. The exponent will be 2.
4. The value will be 25.
So, the exponential form is: 5^2 = 25.