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- Let u = ln a and v = ln b. Write each expression in terms of u and v without using the ln function. ln (b^4√a)
Problem 91
- Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. I = E/R (1- e^(-(Rt)/2), for t
Problem 91
Problem 92
Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. y = K/(1+ae-bx), for b
- Solve each equation. See Examples 4–6. (√2)^(x+4) = 4^x
Problem 93
- Given that log￬10 2 ≈ 0.3010 and log￬10 3 ≈ 0.4771, find each logarithm without using a calculator. log￬10 6
Problem 93
- Let u = ln a and v = ln b. Write each expression in terms of u and v without using the ln function. ln √(a^3/b^5)
Problem 93
- Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. y = A + B(1 - e^(-Cx)), for x
Problem 93
Problem 95
Solve each equation. See Examples 4–6. 1/27 = x-3
- Given that log￬10 2 ≈ 0.3010 and log￬10 3 ≈ 0.4771, find each logarithm without using a calculator. log￬10 3/2
Problem 95
- 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
Problem 95
Problem 95a
Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given g(x) = ex, find g(ln 4)
Problem 95b
Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given g(x) = ex, find g(ln ln 52)
Problem 95c
Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given g(x) = ex, find g(ln 1/e)
Problem 96a
Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = 3x, find ƒ(log3 2)
Problem 96b
Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = 3x, find ƒ(log3 (ln 3))
Problem 96c
Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = 3x, find ƒ(log3 (2 ln 3))
- Given that log￬10 2 ≈ 0.3010 and log￬10 3 ≈ 0.4771, find each logarithm without using a calculator. log￬10 9/4
Problem 97
- Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. A = P (1 + r/n)^(tn), for t
Problem 97
Problem 98a
Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = log2 x, find ƒ(27)
Problem 98b
Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = log2 x, find ƒ(2log_2 2)
Problem 98c
Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = log2 x, find ƒ(22 log_2 2)
- Given that log￬10 2 ≈ 0.3010 and log￬10 3 ≈ 0.4771, find each logarithm without using a calculator. log￬10 √30
Problem 99
- Work each problem. Which of the following is equivalent to 2 ln(3x) for x > 0? A. ln 9 + ln x B. ln 6x C. ln 6 + ln x D. ln 9x^2
Problem 99
Problem 100
Work each problem. Which of the following is equivalent to ln(4x) - ln(2x) for x > 0? A. 2 ln x B. ln 2x C. (ln 4x)/(ln 2x) D. ln 2
Problem 101
Use properties of logarithms to rewrite each function, then graph. ƒ(x) = log2 [4 (x-3) ]
- Use properties of logarithms to rewrite each function, then graph. ƒ(x) = log￬3 [9 (x+2) ]
Problem 102
- 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.
Problem 102
- Use properties of logarithms to rewrite each function, then graph. ƒ(x) = log￬3 x+1/9
Problem 103
Problem 104
To solve each problem, refer to the formulas for compound interest. A = P (1 + r/n)tn and A = Pert 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?
Problem 105
Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = 5^x, g(x) = log￬5 x