Question

sa se determine x stiind ca


Va rog frumos 5 si 3 .Am nevoie urgent dau 32 de puncte si coroana.​

Answer 1

Explicație pas cu pas:

a)

$log_{a}x = 2log_{a}3 - 3log_{a}2 = log_{a}( {3}^{2} ) - log_{a}( {2}^{3} ) = log_{a}9 - log_{a}8 = log_{a} \dfrac{9}{8}$

$\implies x = \dfrac{9}{8}$

b)

$log_{a}x = 3log_{a}(a + b) - 2log_{a}( \sqrt{a + b} ) = log_{a}{(a + b)}^{3} - log_{a} {( \sqrt{a + b} )}^{2} = log_{a}\dfrac{{(a + b)}^{3}}{a + b} = log_{a}{(a + b)}^{2}$

$\implies x = {(a + b)}^{2}$

c)

$log_{a}x = 5log_{a}b + \dfrac{1}{2}\Big[ log_{a}(b + c) + \dfrac{1}{3}log_{a}(b - c) - log_{a}b - log_{a}c \Big] = log_{a} {b}^{5} + \dfrac{1}{2}\Big[ log_{a}(b + c) + log_{a} \sqrt[3]{(b - c)} - log_{a}(bc)\Big] = log_{a} {b}^{5} + \dfrac{1}{2}\Big[ log_{a} \dfrac{(b + c)\sqrt[3]{(b - c)}}{bc} \Big] = log_{a} {b}^{5} + log_{a} \sqrt{\dfrac{(b + c)\sqrt[3]{(b - c)}}{bc}} = log_{a} {b}^{5}\sqrt{\dfrac{(b + c)\sqrt[3]{(b - c)}}{bc}}$

$\implies x = {b}^{5}\sqrt{\dfrac{(b + c)\sqrt[3]{(b - c)}}{bc}}$