Oblicz logarytmy.logPROSZĘ O ROZWIĄZANIE. POTRZEBUJĘ NA JUTRO.:).... Question from @martyparty

November 2018 1 7 Report

Oblicz logarytmy.
log $log_{4} 8 \sqrt[4]{2} \\ log_{ \frac{1}{5} } 25 \sqrt{5} \\ log _{ \sqrt{3} } \sqrt[3]{9}$

PROSZĘ O ROZWIĄZANIE. POTRZEBUJĘ NA JUTRO.
:)

heh Definicja logarytmu:
$log_{a}c=b\ <=>\ a^{c}=b$
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$a) log_{4}8\sqrt[4]{2}=c\ <=>\ 4^{c}=8\sqrt[4]{2}\\
4^{c}=8\sqrt[4]{2}\\
(2^{2})^{c}=2^{3}*2^{\frac{1}{4}}\\
2^{2*c}=2^{3+\frac{1}{4}}\\
2^{2c}=2^{3\frac{1}{4}}$
[Podstawy potęgo po obu stronach są równe, przechodzę więc do działań na wykładnikach potęg]
$2c=3\frac{1}{4}\ |*\frac{1}{2}\\
c=\frac{13}{4}*\frac{1}{2}\\
c=\frac{13}{8}$
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$log_{\frac{1}{5}}25\sqrt{5}=c\ <=>\ (\frac{1}{5})^{c}=25\sqrt{5}\\
(\frac{1}{5})^{c}=25\sqrt{5}\\
(5^{-1})^{c}=5^{2}*5^{\frac{1}{2}}\\
5^{-1*c}=5^{2+\frac{1}{2}}\\
5^{-c}=5^{2\frac{1}{2}}\\
-c=2\frac{1}{2}\ |*(-1)\\
c=-2\frac{1}{2}$
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$log_{\sqrt{3}}\sqrt[3]{9}=c\ <=>\ \sqrt{3}^{c}=\sqrt[3]{9}\\
\sqrt{3}^{c}=\sqrt[3]{9}\\
(3^{\frac{1}{2}})^{c}=9^{\frac{1}{3}}\\
3^{\frac{1}{2}*c}=(3^{2})^{\frac{1}{3}}\\
3^{\frac{1}{2}c}=3^{2*\frac{1}{3}}\\
3^{\frac{1}{2}c}=3^{2\frac{1}{3}}\\
\frac{1}{2}c=2\frac{1}{3}\ |*2\\
c=\frac{7}{3}*2\\
c=\frac{14}{3}$

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Answer

martyparty October 2018 | 0 Replies

WYKONAJ DZIAŁANIA I ZREDUKUJ WYRAZY PODOBNE:1. (x+2)² - (x-3)(x+3)2. (x-4)(x+4) - (2x-1)²3. (x-3)² - (x+1)² 4. (x-2)² - (2x+3)²5. (2x-1)² - (4x-3)²6. (2x+1)² - 3(x+5)²7. ( √2- √3)² - (3 √3-1)(3 √3+1) potrzebuję tego na dzisiaj, więc proszę Was o pomoc:)

Answer

martyparty October 2018 | 0 Replies

OBLICZ:A. |1-√2|B. |√2-2√3|C. |3,14- |D. |2-√2|+|√2-5| E. |√7-4| -|3+√7|F. |√3-√7|G. |2-√7|H. |3-√2|-|√2+1,3|I. |√3+3|-|1-√3|J. 2*|√2-√3|+|√3-2√2|

Answer

WYKONAJ DZIAŁANIA I ZREDUKUJ WYRAZY PODOBNE:1. (x+2)² - (x-3)(x+3)2. (x-4)(x+4) - (2x-1)²3. (x-3)² - (x+1)² 4. (x-2)² - (2x+3)²5. (2x-1)² - (4x-3)²6. (2x+1)² - 3(x+5)²7. ( √2- √3)² - (3 √3-1)(3 √3+1) potrzebuję tego na dzisiaj, więc proszę Was o pomoc:)

OBLICZ:A. |1-√2|B. |√2-2√3|C. |3,14- |D. |2-√2|+|√2-5| E. |√7-4| -|3+√7|F. |√3-√7|G. |2-√7|H. |3-√2|-|√2+1,3|I. |√3+3|-|1-√3|J. 2*|√2-√3|+|√3-2√2|

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