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How do you solve #3^x=500#?

Answer 1

Anna Allen

#x = frac{log(500)}{log(3)}#

First, take the #log# of both sides of the equation to get: #log(3^{x}) = log(500)#

Then use the logarithmic power property to eliminate the exponent: #xlog(3) = log(500)#

Finally, divide both sides of the equation by #log(3)#: #x = frac{log(500)}{log(3)}#

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Answer 2

Lily Anderson

To solve the equation (3^x = 500), you can use logarithms. Specifically, take the logarithm of both sides of the equation with base 3 or base 10.

If using base 3 logarithm:

[ \log_3(3^x) = \log_3(500) ]

[ x = \log_3(500) ]

If using base 10 logarithm:

[ \log(3^x) = \log(500) ]

[ x \cdot \log(3) = \log(500) ]

[ x = \frac{\log(500)}{\log(3)} ]

Using a calculator to evaluate the logarithms, you can find the value of (x).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.