Question

How do you identify the differences between a logarithmic expression, a logarithmic equation, and a logarithmic function? Each has its own related process. Specifically how do you determine what you need to do when faced with one of these problems in algebra?

Answer 1

Logarithmic expression :  A logarithm base b of a positive number x is such that:
for  b > 0, b≠ 1, log_b x = y if and only if b^y = x. So here log_b x = y is logarithmic expression

Logarithmic Equation: Logarithmic equation contains, logarithmic expression with constant. When one side of equation contains logarithm and other side constant then we can solve by rewriting the expression in the form of exponential form.

ex:If log4 x = 5, then x = 4^5

Logarithmic Function: Logarithmic functions are the inverses of exponential functions, and any exponential function can be expressed in logarithmic form. Similarly, all logarithmic functions can be rewritten in exponential form.

If x = 2 ^y , then y = (the power on base 2) to equal x. The word logarithm, abbreviated log, is introduced to satisfy this need.

y = (the power on base 2) to equal x

This equation is rewritten as y = log ₂ x.