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Question Number 35899 by imamu222 last updated on 25/May/18

$$Evaluate{log}_{\sqrt{2}}4+{log}_{1/2}16-{log}_{4}32$$

Commented by Cheyboy last updated on 26/May/18

$${log}_{\sqrt{2}}4+{log}_{1/2}16-{log}_{4}32$$$${log}_{2^{1/2}}4+{log}_{2^{-1}}16-{log}_{2^2}32$$$$2{log}_{2}4-{log}_{2}16-1/2{log}_{2}32$$$${log}_2{4}^2-{log}_{2}16-{log}_2\left(\sqrt{32}\right)$$$${log}_{2}16-{log}_{2}16-{log}_2\left(\sqrt{32}\right)$$$${log}_2(16\mathbf{÷}16\mathbf{÷}\sqrt{32})$$$${log}_2\left(\frac{1}{\sqrt{32}}\right)\Rightarrow {log}_2{2}^{-5}=x$$$$2^{-5/2}=2^x$$$$x=-5/2$$$$$$$$$$

Commented by Cheyboy last updated on 26/May/18

$$oohThankyousiruareright$$$$imademistake$$

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