Matematyka

Bardzo proszę o pomoc, zadanie w załączniku.


Answers

motyllllllll

1 rok temu Comment

Best answer

[latex]log_{a}b=c \ ---\ \textgreater \ \ a^c=b\\ \\ a) \ log_{2}b=5\\ b=2^5=32\\ \\ b) \ \ log_{\frac{1}{2}}b=-1\\ b=(\frac{1}{2})^{-1}=2\\ \\ c) \ \ log_{27}b=\frac{2}{3}\\ b=27^{\frac{2}{3}}=(3^3)^{\frac{2}{3}}=3^2=9\\ \\ d) \ \ log_{7}b=0\\ b=7^0=1\\ \\ e) \ \ log_{\frac{1}{16}}b=-\frac{3}{4}\\ b=(\frac{1}{16})^{-\frac{3}{4}}=[(\frac{1}{2})^4]^{-\frac{3}{4}}=(\frac{1}{2})^{-3}=2^3=8\\ \\ f) \ \ log_{\sqrt{2}}b=-6\\ b=(\sqrt{2})^{-6}=(2^{\frac{1}{2}})^{-6}=2^{-3}=\frac{1}{8}\\ \\ g) \ \ log_{10}b=6\\ b=10^6=1000000\\ \\h) \ \ log_{8}b=-1\\
b=8^{-1}=\frac{1}{8} [/latex]