Equation Solving

[Revsbeck]

Hi,
my calculator say that x=3.5 for this equation. Can anybody help me explaining how to calculate this…. Log ? Rewrite exponent?

5^(x) - 5^(x-2) = 120 * Sqrt(5)
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X=3.5

 

[Otis]

Rewrite exponent?

Hi Revsbeck. Yes, that's one way to begin.

What could we do with this simplified version?

5^x = 5^(3) • 5^(1/2)

Hint: The same property of exponents (shown below) to use on that equation could also be used to begin simplifying your equation.

z^(m+n) = z^m • z^n

 

[Steven G]

Let u = 5^x
5^x-2 = 5^x/25 = u/25
So u - u/25 = 120 * Sqrt(5)
Now solve for u.