Assemble equation log easily

Aug 6th, 2022
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How to assemble equation log

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This lesson focuses on solving basic logarithmic equations. The first equation is log base 2 of 16 equals x, which is converted to exponential form as 2^x = 16, giving x = 4. The second equation is log base x of 81 equals 4, converted to x^4 = 81, resulting in x = 3. The third equation is log base 5 of x equals 3, which is converted to 5^3 = x, giving x = 125.

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We know that the inverse of a log function is an exponential. So, we know that the inverse of f(x) = log subb(x) is f^-1(y) = b^y. If the base is e and we are dealing with the natural log, then the inverse of f(x) = ln(x) is f^-1(y) = e^y.
0:20 1:21 Condensing logarithmic expressions - YouTube YouTube Start of suggested clip End of suggested clip So we have log base 3 of x. Plus log base 3 of y to the fourth thats 3q x cubed. Minus log base 3MoreSo we have log base 3 of x. Plus log base 3 of y to the fourth thats 3q x cubed. Minus log base 3 of z to the fourth.
1) Multiplication inside the log can be turned into addition outside the log, and vice versa. 2) Division inside the log can be turned into subtraction outside the log, and vice versa. 3) An exponent on everything inside a log can be moved out front as a multiplier, and vice versa.
To convert from exponential to logarithmic form, we follow the same steps in reverse. We identify the base b, exponent x, and output y. Then we write x=logb(y) x = l o g b ( y ) .
Explanation: In order to eliminate the log based ten, we will need to raise both sides as the exponents using the base of ten. The ten and log based ten will cancel, leaving just the power on the left side. Change the negative exponent into a fraction on the right side.
0:51 3:14 Rearranging logarithmic equations into exponential equations - YouTube YouTube Start of suggested clip End of suggested clip So theres what this would look like written as an exponent just simply rearranging something thatsMoreSo theres what this would look like written as an exponent just simply rearranging something thats a logarithm into something that were more familiar with and thats an exponent or exponential.

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