6. Exponential & Logarithmic Functions

Solving Exponential and Logarithmic Equations

Textbook Question
In Exercises 93–102, solve each equation. 5^2x ⋅ 5^4x=125
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Textbook Question
In Exercises 93–102, solve each equation. 3^x+2 ⋅ 3^x=81
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Textbook Question
In Exercises 93–102, solve each equation. 2|ln x|−6=0
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Textbook Question
Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. log A = log B - C log x, for A
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Textbook Question
In Exercises 93–102, solve each equation. 3|log x|−6=0
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Textbook Question
In Exercises 93–102, solve each equation. 3^x2=45
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Textbook Question
Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. A = P (1 + r/n)^(tn), for t
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Textbook Question
In Exercises 93–102, solve each equation. ln(2x+1)+ln(x−3)−2 ln x=0
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Textbook Question
In Exercises 93–102, solve each equation. ln 3−ln(x+5)−ln x=0
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Textbook Question
In Exercises 93–102, solve each equation. 5^(x^2−12)=25^2x
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Textbook Question
To solve each problem, refer to the formulas for compound interest. A = P (1 + r/n)^(tn)and A = Pe^(rt)Find t, to the nearest hundredth of a year, if \$1786 becomes \$2063 at 2.6%, with interest compounded monthly.
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Textbook Question
To solve each problem, refer to the formulas for compound interest. A = P (1 + r/n)^tn and A = Pe^rt At what interest rate, to the nearest hundredth of a percent, will \$16,000 grow to \$20,000 if invested for 7.25 yr and interest is compounded quarterly?
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Textbook Question
Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = 5^x, g(x) = log￬5 x
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Textbook Question
Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = log￬2 x+1, g(x) = 2^x-1
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Textbook Question
Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = log￬4 (x+3), g(x) = 4^x + 3
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