document.write( "Question 30488: log2*=x
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document.write( "logex=4 \n" );
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Algebra.Com's Answer #17188 by sdmmadam@yahoo.com(530) ![]() You can put this solution on YOUR website! Probably the problem is \n" ); document.write( "e^x = 4----(1) \n" ); document.write( "Here the base is e, the power is x and the number is 4 \n" ); document.write( "Therefore by definition that log(of a positive quantity N) to a given base b is the power p to which the base b has to be raised to give the number N \n" ); document.write( "Therefore x = log[e](4) \n" ); document.write( "Answer: x = log[e](4)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Note: If you do not understand how to apply the definition \n" ); document.write( "you may proceed as follows too \n" ); document.write( "Taking log on both sides of (1) (base e) \n" ); document.write( "log(e^x) =log(4) \n" ); document.write( "xlog[e](e) = log[e](4) (using log[b](m^n) = nlog[b](m) ) \n" ); document.write( "That is xX1 = log[e](4) \n" ); document.write( "[since log(any positive quantity) to the same base is 1] \n" ); document.write( "That is x = log[e](4) \n" ); document.write( "Answer: x = log[e](4)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Note: Practising the definition and writing down the answer in a jiffy will really help \n" ); document.write( "Examples \n" ); document.write( "1)log[10](100)= x \n" ); document.write( "means 100 = 10^x = 10^2 and therefore x = 2 \n" ); document.write( "2)log[5](125) = t \n" ); document.write( "means 125= 5^x = 5^3 and therefore x = 3 \n" ); document.write( "3)log[2](y) = 5 \n" ); document.write( "means y = 2^5 = 32 \n" ); document.write( "4)log[3](t) = 4 \n" ); document.write( "means t = 3^4 = 81 \n" ); document.write( " |