Construct Equation Log

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How to Construct Equation Log

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The logarithmic function for x = 2y is written as y = log2 x or f(x) = log2 x. The number 2 is still called the base. In general, y = logo x is read, y equals log to the base b of x, or more simply, y equals log base b of x. As with exponential functions, b > 0 and b 1.
To change from exponential form to logarithmic form, identify the base of the exponential equation and move the base to the other side of the equal sign and add the word log. Do not move anything but the base, the other numbers or variables will not change sides.
0:26 3:06 Suggested clip Writing Logarithmic Equations In Exponential Form — YouTubeYouTubeStart of suggested client of suggested clip Writing Logarithmic Equations In Exponential Form — YouTube
How To: Given an equation in logarithmic form logo(x)=y l o g b (x) = y, convert it to exponential form. Examine the equation y=log bx y = l o g b x and identify b, y, and x. Rewrite log bx=y l o g b x = y as by=x b y = x.
How To: Given an equation of the form y = A e k t \\display style y=A{e}^{kt} y=AEK, solve for t. Divide both sides of the equation by A. Apply the natural logarithm of both sides of the equation. Divide both sides of the equation by k.
The logarithmic function for x = 2y is written as y = log2 x or f(x) = log2 x. The number 2 is still called the base. In general, y = logo x is read, y equals log to the base b of x, or more simply, y equals log base b of x. As with exponential functions, b > 0 and b 1.
Logarithm product rule. Logb(x × y) = logo(x) + logo(y) Logarithm quotient rule. Logb(x / y) = logo(x) — logo(y) Logarithm power rule. Logb(x y) = y A logo(x) Logarithm base switch rule. Logb(c) = 1 / logic(b) Logarithm base change rule. Logb(x) = logic(x) / logic(b) Logarithm — log(x) See also.
Type the number you're working with into your graphing or scientific calculator. For example, type “1000.” Press the “Log” button on your calculator. The number you immediately see is the exponent for the original number you entered. ... Check your work.
A logarithm is the power to which a number must be raised in order to get some other number (see Section 3 of this Math Review for more about exponents). For example, the base ten logarithms of 100 is 2, because ten raised to the power of two is 100: log 100 = 2.
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