L23 - Lecture 23: Section 3.4 Exponential and Logarithmic...

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Unformatted text preview: Lecture 23: Section 3.4 Exponential and Logarithmic Equations Two basic strategies for solving exponential or logarithmic equations: 1. One-to-One Properties u1D44E u1D465 = u1D44E u1D466 if and only if log u1D44E u1D465 = log u1D44E u1D466 if and only if 2. Inverse Properties u1D44E log u1D44E u1D465 = log u1D44E u1D44E u1D465 = ex. Solve for u1D465 : 1) 2 u1D465 = 64 2) ln u1D465 2 ln 2 = 0 3) u1D452 u1D465 = 5 4) log u1D465 = 2 Solving Exponential Equations 1. Isolate the exponential expression on one side of the equation. 2. Take the logarithm of each side, then use the Properties of Logarithms to bring down the expo- nent. 3. Solve for the variable. ex. Solve for u1D465 : 1) 3 u1D452 2 u1D465 = 5 2) 5 u1D465 2 = 2 ex. Solve for u1D465 : 5 u1D465 1 = 3 2 u1D465 ex. Solve for u1D465 : u1D452 2 u1D465 u1D452 u1D465 6 = 0 Solving Logarithmic Equations 1. Isolate the logarithmic term on one side of the equation; you may need to first combine the logarithmic terms.logarithmic terms....
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L23 - Lecture 23: Section 3.4 Exponential and Logarithmic...

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