[tex]a)\\\\(\log0,08+3\log0,5)^{-3}=(\log0,08+\log0{,}5^3)^{-3}=[\log(0,08\cdot0,125)]^{-3}=\\\\=(\log0,1)^{-3}=(\log10^{-1}})^{-3}=(-1\log10})^{-3}=(-1)^{-3}=-1\\\\\\ b)\\\\\big7^{\,2\,+\,\log_{49}25}=\big7^2\cdot\big7^{\log_{49}25}= 49\cdot\big(\sqrt{49}\big)^{\log_{49}25}= 49\cdot\big(49}^\frac12 \big)^{\log_{49}25} =\\\\= 49\cdot4 \big9^{\frac12\log_{49}25} = 49\cdot4\big9^{\log_{49}25^\frac12} =49\cdot2\big5^\frac12 =49\cdot5=245[/tex]
[tex]c)\\\\\log_30,375-\log_3\frac18=\log_3(0,375:\frac18)=\log_3(\frac38\cdot\frac81) = \log_33=1\\\\\\ d)\\\\\log_4^23-\log_49\cdot\log_46+\log_4^26=\log_4^23-\log_43^2\cdot \log_46 +\log_4^26=\\\\=(\log_43)^2-2\cdot\log_43\cdot \log_46+(\log_46)^2= (\log_43-\log_46)^2=\\\\=\big(\log_4\frac36\big)^2=\big(\log_4\frac12\big)^2= \big(\log_4(\frac14)^\frac12\big)^2=\big(\log_44^{-\frac12}\big)^2= \big(-\frac12\log_44\big)^2 = \\\\ =\big(-\frac12\big)^2=\frac14[/tex]
