Solving logarithmic equations Video transcript Solve 4 is equal to log base b of 81 for b. So let's just remind ourselves what this equation is saying. This is saying, if I raise b to the fourth power, then I'm going to get Let me rewrite that. So if I raise b, that's our base, so if I raise our base, b-- I guess that's why they picked b.
If I raise b to the fourth power-- I'll do the fourth power in orange. If I raise b to the fourth power, that is going to be equal to I've just rewritten this equation, this logarithmic equation, I've rewritten it as an exponential equation. So it says b to the fourth power is equal to 81, and we need to still solve for b.
So you just have to think, what number do I have to multiply by itself four times in order to get And 81 might jump out of you, it is a perfect square. We know that 9 times 9 is equal to Or we know that another way to say that is, nine squared is equal to But we have to raise something to the fourth power.
But 9 itself is 3 times 3. So one 9 is 3 times 3, and then you multiply it by another 9. That's another 3 times 3. That will also be equal to And we can verify it. So this is 3 to the fourth power. So there we've done it. We've said, well, some number to the fourth power is equal to We know that 3 to the fourth power is equal to So we know that b is equal to 3.
Or we could say, log base three of 81, this is saying what power do I have to raise 3 to, to get 81? Well, we know. You have to raise 3 to the fourth power to get to And if you know about fractional exponents, and don't worry about this if this confuses you a little bit, you could raise both of these, if you know about fractional exponents and exponent properties, you could do it this way as well.
You could take, so you have b to the fourth power is equal to Anything you do to one side of equation, you have to do to the other side.
Or this is, essentially, just raising it to the first power. What do I have to raise to the fourth power to get to 81? But if this is confusing to you, don't worry about it for now. The important thing is you understand what the logarithm is actually saying. If I raise b to the fourth power I get You're welcome!
Let me take a look You'll be able to enter math problems once our session is over. Algebra Examples. Step-by-Step Examples. Algebra. Write in Exponential Form. For logarithmic equations, is equivalent to such that,, and. In this case,,, and. Substitute the values of,, and into the equation.
Enter YOUR Problem. About;. Changing from Exponential Form to Logarithmic Form To learn how to change an equation from exponential form to logarithmic form, let’s look at a specific example.
Consider the exponential equation 5 x = 25, what would this equation look like in logarithmic form? The equation 5 x. Changing from Exponential Form to Logarithmic Form – Practice Problems Move your mouse over the "Answer" to reveal the answer or click on the "Complete Solution" link to reveal all of the steps required to change from exponential form to logarithmic form.
Write the exponential equation x 6 = in logarithmic form.
Complete Solution. Sep 23, · Find an answer to your question Write the equation in logarithmic form. 2^5 = 32 A. log32 = 5 • 2 B. log = 5 C. log32 = 5 D. log = 2. Jul 05, · Write the equation in logarithmic form. Write the equation in logarithmic form.
|Purplemath||Writing and evaluating logarithms Video transcript Voiceover:Rewrite the following equation in logarithmic form.|
|Logarithmic equations: variable in the base (video) | Khan Academy||Exponents, Logarithms, and Inverse Functions Search for: Introduction to Exponents and Logarithms Introduction to Exponential and Logarithmic Functions Logarithmic functions and exponential functions are inverses of each other. That is, they undo each other.|
|Rewrite as a logarithmic equation e^9=y | Wyzant Ask An Expert||Study each case carefully before you start looking at the worked examples below. Types of Logarithmic Equations The first type looks like this.|
Skip navigation Sign in. Re-writing logarithmic equations in exponential form - Duration: Solving Logarithmic Equations Deciding How to Solve Logarithmic Equation When asked to solve a logarithmic equation such as or the first thing we need to decide is how to solve the problem.
Some logarithmic problems are solved by simply.