Question

Convert the following to following forms: (a) Exponential Form: y = log3 2x (b) Logarithmic Form: −2 · 8 x 2+1 = −10

Answer 1

The exponential form of y = log3 2x is 3^y = 2x. The transition from the provided exponential form to a logarithmic form may have errors as the transformed equation is x = 11/16, which is not in the form logb x = y.

Step-by-step explanation:

To convert an equation from logarithmic form to exponential form, you can follow this rule: y = logbx can be rewritten as by = x. So for your example y = log32x, the exponential form would be 3y = 2x.

Moving on to converting equations from exponential form to logarithmic form, you would use this rule: if by = x, then logbx = y. The given equation has some amounts that needs simplifying first: -2 · 8 x 2+1 = -10. We can change this to -16x+1=-10, then to -16x=-11, and finally x = 11/16. However this approach does not result in a logarithmic form and it seems there might be some errors in the equation provided.

Learn more about Logarithmic and Exponential Form