# Art of problem solving intermediate algebra

This Art of problem solving intermediate algebra provides step-by-step instructions for solving all math problems. We will also look at some example problems and how to approach them.

## The Best Art of problem solving intermediate algebra

We'll provide some tips to help you select the best Art of problem solving intermediate algebra for your needs. This formula states that the log of a number with respect to one base is equal to the log of the same number with respect to another base multiplied by the log of the new base with respect to the old base. So, if we want to solve for x in our example equation above, we can plug in our known values and solve for x using algebra.2log₃x=6⇒log₃x=3⇒x=33Since we now know that 3 was raised to the third power in order to produce 9 (our exponent), we have successfully solved for x in this equation!Common and natural logarithms are two other ways that exponents can be solved for without using the change of base formula. Common logarithms use bases of 10, while natural logarithms use bases of e (approximately 2.71828182845904). To solve for x in equations using these types of logs, all you need to do is take the inverse function of each side. For example, if we want to solve10log₁₀x=100we can simply take the inverse common log function of both sides.This tells us that 100 must have been produced when 10 was raised to some power - but what power? Well, we can use algebra once again!10log₁₀x=100⇒log₁₀x=10⇒x=1010Now we know that 10 was raised to the 10th power in order to produce 100. And just like that - we've solved another equation for x using logs!While solving equations with logs may seem daunting at first, there's no need to worry - with a little practice, you'll be a pro in no time!

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