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igomit [66]
3 years ago
7

I need help!!

Mathematics
1 answer:
Natasha2012 [34]3 years ago
7 0

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

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