2. Use the change-of-base formula to convert each logarithm to an expression involving logarithms with the specified new base: (a) $\log_2 3$ in base 3. (b) $\log_6 12$ in base 17 (c) $\ln e$ in base 2
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Step 1: The change-of-base formula states that for any positive numbers a, b, and x, where a ≠ 1 and b ≠ 1, we have: log$_a$ x = (log$_b$ x) / (log$_b$ a) Show more…
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(a) Derive the general change of base formula $$ \log _{b} x=\frac{\log _{a} x}{\log _{a} b} $$ (b) Use the result in part (a) to find the exact value of $\left(\log _{2} 81\right)\left(\log _{3} 32\right)$ without using a calculating utility.
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Exponential and Logarithmic Functions
(a) 3log3(6) (b) 4log4(22) (c) e^ln(10) = 10
Joy D.
(a) Derive the general change of base formula $$\log _{b} x=\frac{\log _{a} x}{\log _{a} b}$$ (b) Use the result in part (a) to find the exact value of $\left(\log _{2} 81\right)\left(\log _{3} 32\right)$ without using a calculating utility. IHint: Take $x=a .1$
Logarithmic and Exponential Functions
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