# How do you solve #10^ { x } \cdot e ^ { x } = 3#?

Take the natural log of both sides

Using the following property of logarithms we can rewrite the left hand side

Using another property of logarithms we can rewrite the left hand side again

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To solve the equation (10^x \cdot e^x = 3), you can take the natural logarithm of both sides to eliminate the exponentials. After applying logarithm, you will get an equation in terms of (x), which can then be solved for (x). The solution will involve the Lambert W function, a special function that arises in the solution of certain transcendental equations. The solution for (x) will be expressed as (x = W(c)), where (W) is the Lambert W function and (c) is a constant.

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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.

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.

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.

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