To find the value of y in the equation 5y = 12, we first need to isolate y. This involves using logarithms, which can help us solve equations involving an exponent.
Starting with the equation:
5y = 12
To solve for y, we can express the equation in logarithmic form. First, we divide both sides by 5:
y = 12 / 5
Next, we calculate this value:
y = 2.4
However, to visualize it graphically using logarithms, we can express the equation in a different form. We can rewrite it as:
y = log5(12)
To approximate this value using a logarithmic graph, we would use the graph of y = logb(x) where b is the base of the logarithm.
For this specific case, we can transform log5(12) to a more commonly used base.
Using the change of base formula:
logb(x) = logk(x) / logk(b)
For instance, if we choose base 10:
y = log10(12) / log10(5)
This means you would use a logarithmic graph of base 10 to find the approximate value of y. By locating the point on the graph corresponding to x = 12 and applying the logarithm base 10 for both 12 and 5, you can derive y visually as well as numerically. Thus, the logarithmic graph that can be employed to approximate the value of y in the equation 5y = 12 leans predominantly on the logarithm of bases 5 or 10, depending on the accessibility of the logarithmic scale displayed on the graph.