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

Evaluate log_(√2) 4+log_(1/2) 16−log_4 32

$${Evaluate}\:{log}_{\sqrt{\mathrm{2}}} \mathrm{4}+{log}_{\mathrm{1}/\mathrm{2}} \mathrm{16}−{log}_{\mathrm{4}} \mathrm{32} \\ $$

Commented by Cheyboy last updated on 26/May/18

log_(√2) 4+log_(1/2) 16−log_4 32 log_2^(1/2) 4+log_2^(−1) 16−log_2^2 32 2log_2 4−log_2 16−1/2log_2 32 log_2 4^2 −log_2 16−log_2 ((√(32))) log_2 16−log_2 16−log_2 ((√(32))) log_2 (16÷16÷(√(32))) log_2 ((1/(√(32))))⇒log_2 2^(−5) =x 2^(−5/2) =2^x x= −5/2

$${log}_{\sqrt{\mathrm{2}}} \mathrm{4}+{log}_{\mathrm{1}/\mathrm{2}} \mathrm{16}−{log}_{\mathrm{4}} \mathrm{32} \\ $$$${log}_{\mathrm{2}^{\mathrm{1}/\mathrm{2}} } \mathrm{4}+{log}_{\mathrm{2}^{−\mathrm{1}} } \mathrm{16}−{log}_{\mathrm{2}^{\mathrm{2}} } \mathrm{32} \\ $$$$\mathrm{2}{log}_{\mathrm{2}} \mathrm{4}−{log}_{\mathrm{2}} \mathrm{16}−\mathrm{1}/\mathrm{2}{log}_{\mathrm{2}} \mathrm{32} \\ $$$${log}_{\mathrm{2}} \mathrm{4}^{\mathrm{2}} −{log}_{\mathrm{2}} \mathrm{16}−{log}_{\mathrm{2}} \left(\sqrt{\mathrm{32}}\right) \\ $$$${log}_{\mathrm{2}} \mathrm{16}−{log}_{\mathrm{2}} \mathrm{16}−{log}_{\mathrm{2}} \left(\sqrt{\mathrm{32}}\right) \\ $$$${log}_{\mathrm{2}} \left(\mathrm{16}\boldsymbol{\div}\mathrm{16}\boldsymbol{\div}\sqrt{\mathrm{32}}\right) \\ $$$${log}_{\mathrm{2}} \left(\frac{\mathrm{1}}{\sqrt{\mathrm{32}}}\right)\Rightarrow{log}_{\mathrm{2}} \mathrm{2}^{−\mathrm{5}} ={x} \\ $$$$\mathrm{2}^{−\mathrm{5}/\mathrm{2}} =\mathrm{2}^{{x}} \\ $$$${x}=\:−\mathrm{5}/\mathrm{2} \\ $$$$ \\ $$$$ \\ $$

Commented by Cheyboy last updated on 26/May/18

ooh Thank you sir u are right i made mistake

$${ooh}\:{Thank}\:{you}\:{sir}\:{u}\:{are}\:{right}\: \\ $$$${i}\:{made}\:{mistake} \\ $$

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