Question #84146

What is value for x in the equation below?
10^(7.82x) = 381.7(8.56+7.31)
Note: Logarithms and exponentials will feature prominently throughout the course and understanding how to solve these types of equations (and knowing how to use your calculator) is essential.

Expert's answer

10^7.28x = 381.7(8.56+7.31)

So, at first let‘s open brackets at the right side:

10^7.28x = 6 057.579

There is a main method, when:

A^f(x) = B, and f(x) = logAB.

Let’s use it: 7.28x = log_10(6057.579) (on many calcs log10 is “lg”)

7.28x = 3.782

x = 3.782/7.28 ~ 0.5195

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