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Solving exp_log equations

# Solving exp_log equations - 10 20(apply the property of...

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MAC1105: Solving Exponential and Logarithmic Equations Functions x y 10 = and y logx = are inverses of one another. Similar to addition/subtraction and multiplication/division, each function provides an operation that can be used to solve equations involving the other. The same is true for functions x y e = and y lnx = . This is summarized by: x logx x lnx log10 x and 10 x lne x and e x = = = = Examples: 1) Solve the equation x 10 50 = . 2) Solve the equation x e 50 = . x x log log 10 50 10 50 x log 50 x 1.7 = = = x x e 50 e 50 x ln 5 ln ln 0 x 3.9 = = = 2) Solve the equation log(5x) 2 = . 4) Solve the equation ln(5x) 2 = . log(5x) 2 10 10 5x 100 x 20 = = = ln(5x) 2 2 2 5x e e x 1.48 e 5 e = = = 5) Solve the equation x 5(10 ) 32 68 - = . x x x x 5(10 ) 32 68 (add 32 to both sides) 5(10 ) 100 (divide both sides by 5) 10 20 (apply the common log function to both sides)
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Unformatted text preview: 10 20 (apply the property of inverses to the left side) x log 20 (exact value) x 1.3 (one dec l i o mal plac g l e app og-= = = = = ≈ roximation) 6) Solve the equation 7 ln(4x) 2-=-= . x ln(4x) 5 5 5 7 ln(4x) 2 (subtract 7 from both sides) ln(4x) 5 (multiply both sides by 1) ln(4x) 5 (apply the e function to both sides) (apply the property of inverses to the left side) 4x e (divide both sides by 4) e x (exact value) 4 e e x-=-=-= ---= --= = = = 37.1 (one decimal place approximation) ≈...
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