*And this is really straight derived from these two right over here.*

We're asked to solve the log of x plus log of 3 is equal to 2 log of 4 minus log of 2. So we have the log of x plus the log of 3 is equal to 2 times the log of 4 minus the log of 2, or the logarithm of 2. Whenever you see a logarithm written without a base, the implicit base is 10.

So we could write 10 here, 10 here, 10 here, and 10 here.

Round-off error can get really big really fast with logs, and you don't want to lose points because you rounded too early and thus too much. In other words, when you plug your decimal approximation into the original equation, you're just making sure that the result is close enough to be reasonable.

For instance, to check the solution of the equation No, the two values are not equal, but they're pretty darned close.

An example would be: , is a valid solution, and often this will be all that I'm supposed to give for the answer.

However, in this case (maybe leading up to graphing or word problems) they want me to provide a decimal approximation.

This is going to be equal to log base 10 of 16 over 2, 16 divided by 2, which is the same thing as 8. And 10 to the same power is going to be equal to 8. 3x is equal to 8, and then we can divide both sides by 3.

So the right-hand side simplifies to log base 10 of 8. Divide both sides by 3, you get x is equal to 8 over 3.

Allowing for round-off error, these values confirm to me that I've gotten the right answer.

If, on the other hand, my solution had returned a value of, say, Let's do a couple more examples. is the answer, I first need to check (especially because this answer is negative) whether it'll work in the original equation.

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## How to Solve Logarithmic Equations - dummies

In this type of log equation, the variable you need to solve for is inside the log, but the equation has more than one log and a constant. You can solve equations with more than one log. To solve log 2 x – 1 + log 2 3 = 5, for instance, first combine the two logs that are adding into one log by using the product rule…

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## Solving Log Equations Calculator Considerations & Examples.

Solve log2 x = 4.5, accurate to two decimal places. By the way, when finding approximations with your calculator, don't round as you go along. Instead, do all the solving and simplification algebraically; then, at the end, do the decimal approximation as one possibly long set of commands in the calculator.…

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Video transcript. The left-hand side is log base 10 of 3x. So if 10 to some power is going to be equal to 3x. And 10 to the same power is going to be equal to 8. So 3x must be equal to 8. 3x is equal to 8, and then we can divide both sides by 3. Divide both sides by 3, you get x is equal to 8 over 3.…

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## Solving Logarithmic Equations - Math Help Online Math.

The problems in this lesson involve solving logarithmic equations. To learn how to solve logarithmic equations, we start by simply converting the equation from logarithmic to exponential form. For example, when solving logarithmic equations such as 'log base x of 144 equals 2,' we switch from logarithmic to exponential form, to get x^2 = 144, or x = plus or minus 12.…

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Step 1 Use Known Log Rules. In any problem that involves solving logarithmic equations, the first step is to always try to simplify using the log rules. In this case, we will use the product, quotient, and exponent of log rules. We do this to try to make a polynomial/algebraic equation that is easier to solve.…