Mth141s55 - Sec 5.5 Solving Exponential and Logarithmic...

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Sec. 5.5 – Solving Exponential and Logarithmic Equations To solve exponential equations there are two techniques generally used : 1) If the value that the exponential expression is equal to is a power of the same base, get the bases the same. If the bases are the same and the expressions are equal, then the exponents must be equal!! We did these in Sec. 5.2 !! 2) If the value that the exponential expression is equal to is NOT a power of the base, then convert to its log form and solve for x by using the change of base property. Ex1. 2 7 x = 2 log 7 x = now use change of base. log7 log2 x = .84509804 2.807354922 .3010299957 x = = Another technique is to take the log of both sides of the original equation. If they are equal, then there logs should be equal (since they are 1-1 functions!). 2 7 x = log 2 log7 x = (Note : using base of 10 for the log.) log 2 log7 x = log7 log 2 x = (same equation we got above the other way!) .84509804 2.807354922 .3010299957 x = =
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Ex2. 2
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This note was uploaded on 06/06/2011 for the course MTH mth141 taught by Professor Stean during the Spring '10 term at Moraine Valley Community College.

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Mth141s55 - Sec 5.5 Solving Exponential and Logarithmic...

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