Question

I need help!!

Solve the equation. Give the exact solution and an approximate solution to three decimal places.

5^(7x) = 60

Answer 1

Answer:

The exact solution is

$x = \frac{Ln(60)}{7*Ln(5)}$

And the approximation to three decimal places is:

x = 0.363

Step-by-step explanation:

Here we have the equation:

$5^{7*x} = 60$

Now we can remember a property of the natural logarithm function:

Ln(a^n) = n*Ln(a)

Now we can apply the Ln( ) function to both sides of that equation to get:

$Ln(5^{7*x}) = Ln(60)$

Then we get:

$7*x*Ln(5) = Ln(60)$

Solving that for x we get:

$x = \frac{Ln(60)}{7*Ln(5)} = 0.363$

So the exact solution is:

$x = \frac{Ln(60)}{7*Ln(5)}$

And the approximation to three decimal places is:

x = 0.363