Solve each equation. (√2)^x+4 = 4^x

Given that log₁₀ 2 ≈ 0.3010 and log₁₀ 3 ≈ 0.4771, find each logarithm without using a calculator. log₁₀ 6

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. y = A + B(1 - e^-Cx), for x

Given that log₁₀ 2 ≈ 0.3010 and log₁₀ 3 ≈ 0.4771, find each logarithm without using a calculator. log₁₀ 3/2

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. log A = log B - C log x, for A

Solve each equation. See Examples 4–6. 1/27 = x^-3

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given g(x) = e^x, find g(ln 4)

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given g(x) = e^x, find g(ln ln 5²)

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given g(x) = e^x, find g(ln 1/e)

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = 3^x, find ƒ(log₃ 2)

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = 3^x, find ƒ(log₃ (ln 3))

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = 3^x, find ƒ(log₃ (2 ln 3))

Given that log₁₀ 2 ≈ 0.3010 and log₁₀ 3 ≈ 0.4771, find each logarithm without using a calculator. log₁₀ 9/4

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. A = P (1 + r/n)^tn, for t

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)

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = log₂ x, find ƒ(2^{log_2 2})

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = log₂ x, find ƒ(2^{2 log_2 2})

Given that log₁₀ 2 ≈ 0.3010 and log₁₀ 3 ≈ 0.4771, find each logarithm without using a calculator. log₁₀ √30

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 9x²

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

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) = log₃ [9 (x+2) ]

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.

Use properties of logarithms to rewrite each function, then graph. ƒ(x) = log₃ (x+1)/9

Use properties of logarithms to rewrite each function, and describe how the graph of the given function compares to the graph of g(x) = ln x. ƒ(x) = ln(e²x)

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?

Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = 5^x, g(x) = log￬5 x

Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = log￬2 x+1, g(x) = 2^x-1

Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = log￬4 (x+3), g(x) = 4^x + 3

Write an equation for the inverse function of each one-to-one function given. ƒ(x) = 3^x