Using the Graph of f(x) = log10(x) to Approximate the Value of y in the Equation 10y = 4 log base 10

To solve the equation 10y = 4 log₁₀(x), we need to first isolate the variable y on one side of the equation. This can be done by dividing both sides by 10:

y = (4 log₁₀(x)) / 10

Now we can simplify this to:

y = (2/5) log₁₀(x)

Next, we need to use the graph of f(x) = log₁₀(x) to find the value of log₁₀(x) at a specific x-value. Let’s assume we select a value for x that is visible on the graph.

For instance, if we choose x = 100 (which is a common value), we can look at the graph or calculate:

log₁₀(100) = 2

Substituting this value back into our equation for y gives:

y = (2/5) * 2 = 4/5 = 0.8

Therefore, by analyzing the graph and using our derived equation, we approximate that when x = 100, the value of y is approximately 0.8.