Evaluate each expression without a calculator.

Question

a. log₁₀ 1000

Accepted Answer

Hello there, today we're gonna solve the following practice problem together. So first stop, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem, evaluate the expression log base two of 32 without using a calculator. Awesome. So our end goal, our final answer that we're ultimately trying to solve for is we're trying to evaluate the specific log expression. Awesome. So now that we know that we're trying to evaluate this log expression, let's read off our multiple choice answers to see what our final answer might be. A is four. B is five, C, is six and D is three. Awesome. So first off, we need to identify our expression that we're trying to evaluate which once again our E expression that we're trying to evaluate is log base two of 32 and we need to take log base two of 32. And now at this point, we need to recall and use the definition of a logarithm, which as we should recall and note the definition of a logarithm states that log base B of A is equal to C which means that B to the power of C is equal to A. So now our next step is we need to set up the equation based on the definition which when we do that, when you take two to the power of C is equal to 32 because our base is two, that's why we have two to the power of C. So our next step now is we need to express 32 as a power of two, which means if we say 32 is equal to two to the power of five, we as two multiplied by 25 times is equal to 32. So now we need to substitute in two to the power of 5432. So that will mean that two to the power of C is equal to two to the power of five. So therefore, without a doubt that since the bases are the same, we can set the exponents equal to each other, which will mean that we can safely say that C is equal to five. So therefore, without a doubt, log base two of 32 will be equal to five. And that is our final answer. Hooray, we did it and this corresponds with multiple choice answer letter B which once again is five. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

Evaluate each expression without a calculator.

a. log₁₀ 1000

Key Concepts

Logarithms

Base of a Logarithm

Properties of Logarithms

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