Write the logarithmic equation in exponential form, or write the exponential equation in logarithmic form. 3^5 = 243 Write the logarithmic equation in exponential form, or write the exponential equation in logarithmic form. (1/2)^-3 = 8 Write the logarithmic equation in exponential form, o...
Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ay. y = logax only under the following conditions: x = ay, a > 0,...
To solve an exponential equation, logarithms of both sides of the equation are taken and converted to the equivalent exponential form to solve a logarithmic equation. Exponential functions occur in a wide variety of applied problems. This chapter presents problems dealing with population growth such ...
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(1)Interchange x and y:(2)Make y the subject of the equation:x=byy=logbx(1)Interchange x and y:x=by(2)Make y the subject of the equation:y=logbx Therefore, if we have the exponential function f(x)=bxf(x)=bx, then the inverse is the logarithmic function f−1(x)=logbxf...
(1/2) x . Solution: Chapter4:ExponentialandLogarithmicFunctions 4.1ExponentialFunctions Example3–GraphingExponentialFunctionswith01 Sketch the graph of y = log 2 x. Solution: 2007 Pearson Education Asia - 14 Chapter 4: Exponential and Logarithmic Functions 4.2 Logarithmic Functions Example 5 – ...
We use the fact that if two quantities are equal, the logarithm of these quantities will also be equal. Thus if ex=5 then ln ex=ln 5. Using property 3, ln ex=x so our equation becomes x=ln5,which is the solution. Or, to review the steps: ...
What is logarithmic differentiation? Give an example. Given that y = ae^x, take the natural logarithm on both sides. Let Y = ln(y). Consider Y as a function of x. What kind of function is Y ? Write the exponential equation in logarithmic form. For example...
It follows from equation (2) that the exponential function of a complex variablezhas a period 2πi; that is,ez+ 2πi=ezore2πi= 1. The derivative of the exponential function is equal to the function itself: (ez)ʹ =ez. These properties of the exponential function account for its ...
【解析】For logarithmic equations, log,(r)=y is equivalent to b^y=x such that x0 , b0 , and b≠1. In this,b=,x=m, an y=(log_a(m))/(log_a(b))=my=(log_a(m))/(log_a(b)) Substitute the values of b, s, and y into the equation=x.b^((log_0(m))/)(log_a(...