Zadanie 17
a)
log_3x=2+2log_32
log_3x=log_33^2+log_32^2
log_3x=log_3(9*4)
log_3x=log_336
x=36
b)
logx=-1+2log5
logx=log\frac{1}{10}+log5^2
logx=log(0,1*25)
logx=log2,5
x=2,5
c)
log_{0,5}x=1+log_{0,5}6-2log_{0,5}3
log_{0,5}x=log_{0,5}0,5+log_{0,5}6-log_{0,5}3^2
log_{0,5}x=log_{0,5}(0,5*6)-log_{0,5}9
log_{0,5}x=log_{0,5}\frac{3}{9}
log_{0,5}x=log_{0,5}\frac{1}{3}
x=\frac{1}{3}
d)
log_{\sqrt2}x=4-2log_{\sqrt2}6+3log_{\sqrt2}3
log_{\sqrt2}x=log_{\sqrt2}(\sqrt2)^4-log_{\sqrt2}6^2+log_{\sqrt2}3^3
log_{\sqrt2}x=log_{\sqrt2}((\sqrt2)^2)^2-log_{\sqrt2}36+log_{\sqrt2}27
log_{\sqrt2}x=log_{\sqrt2}\frac{4}{36}+log_{\sqrt2}27
log_{\sqrt2}x=log_{\sqrt2}(\frac{1}{\not9^3}*\not27^9)
log_{\sqrt2}x=log_{\sqrt2}\frac{9}{3}
log_{\sqrt2}x=log_{\sqrt2}3
x=3