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• Exponents and Logarithms
• Logarithm tests
• Logarithm definition

# Logarithm definition

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•  Question 1: 1 pts Logarithmic functions is the inverses of exponential functions.
•  Question 2: 1 pts $\log_{b}(x)=y\Leftrightarrow b^{y}=x$
•  Question 3: 1 pts If $f(x)=a^{x}$ and $g(x)=\log_{a}x$ then $f$ and $g$ have the same domain.
•  Question 4: 2 pts $$\log 17= \log_{10}17$$
•  Question 5: 2 pts Find the inverse of the exponential function $2^{x}=8.$
 $x=\log_{2}8$ $x=\log_{8}2$ $2=\log_{x}8$ $8=\log_{2}x$
•  Question 6: 2 pts Find the inverse of the exponential function $y=3^x.$
 $x = log_y3$ $x = 3logy$ $x = log_3y$ $x = y log3$
•  Question 7: 2 pts Find the domain of the function given by $y=\log\left(\dfrac{4-x}{2}\right)-3$
 $(4,+\infty)$ $(-\infty,4)$ $(-4,4)$ $(-4,+\infty)$
•  Question 8: 3 pts Find the correct logarithmic equation. $$\pi^{4}=x$$
 $\log_{4}x=\pi$ $\log_{\pi}4=x$ $\log_{x}\pi=4$ $\log_{\pi}x=4$
•  Question 9: 3 pts Find the correct exponential equation. $$\log_{7}x=5$$
 $x = 5^{7}$ $x = 7^{5}$ $7^{x}=5$ $7x^{5}=7$
•  Question 10: 3 pts Solve. $$\log_{2}x=9$$
 $2$ $9$ $x=81$ $x=512$