Part 2/7:
However, solving for ( y ) in this instance is not straightforward using basic algebra. To navigate this, we utilize the concept of logarithms. The logarithm essentially acts as the inverse operation of exponentiation. Thus, if ( x = a^y ), then we can express ( y ) as:
[
y = \log_a(x)
]
This relationship highlights the definition of logarithms: they allow us to transform an exponential equation into a format that is easier to manipulate and solve.
Graphing Logarithmic Functions
Graphically, the logarithmic function is an inverse of the exponential function. When you graph ( y = a^x ) and ( y = \log_a(x) ) on the same set of axes, you'll notice that they are reflections of each other across the line ( y = x ).