Final answer:
To convert an exponential equation to a logarithmic form, you rewrite the exponent as a logarithm: y = b^x becomes logb(y) = x. For converting back to an exponential form, reverse the process: logb(y) = x becomes y = b^x. Use the log and ln buttons on your calculator for common and natural logarithms, respectively, and calculate 10^x or e^x for their inverses.
Step-by-step explanation:
To convert between exponential form to logarithmic form, you must understand the relationship between exponents and logarithms. When you have an equation in the form of y = b^x, you can write its logarithmic form as logb(y) = x, where b is the base of the logarithm. Similarly, to go from a logarithm to an exponential form, if you have logb(y) = x, you can write it as y = b^x.
To obtain the common logarithm of a number, simply use the log button on your calculator. If you have the logarithm and wish to find the number it represents, calculate 10^x where x is the value of the logarithm. This operation is often referred to as taking the inverse log.
In the case of the natural logarithm, use the ln button on your calculator. To find the value of a number given its natural logarithm, calculate e^x where x is the natural logarithm. The natural logarithm and the exponential function e^x are inverses, so ln(e^x) = x and vice versa.
The use of logarithms and exponential numbers in calculations is highly useful in various scientific and mathematical contexts, such as computing attributes of growth or in the integrated rate law for chemical reactions.