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What is [log, base 3b(3b again but regular number)exponent 5] times [log, base 11 1]?\r
\n" ); document.write( "\n" ); document.write( "Solve for b: 7log b=3\r
\n" ); document.write( "\n" ); document.write( "Solve for d: 4ln(4d-2)=6\r
\n" ); document.write( "\n" ); document.write( "Please give me the steps so I know how to do them.\r
\n" ); document.write( "\n" ); document.write( "log, base 3b(3b again but regular number)exponent 5] times [log, base 11 1]?\r
\n" ); document.write( "\n" ); document.write( "log[(3b)^5] X log(1) (using log(b)^m to the base (b) = m log(b) to the base b
\n" ); document.write( "(3b) 11\r
\n" ); document.write( "\n" ); document.write( "and log anything to the same base is 1 and hence 5X1 = 5 and log(1) to any base is zero )\r
\n" ); document.write( "\n" ); document.write( "=5 X 0
\n" ); document.write( "=0\r
\n" ); document.write( "\n" ); document.write( "Solve for b: 7log b=3
\n" ); document.write( "Quick way of doing this is dividing by 7 and then applying definition of logarithm of a positive number
\n" ); document.write( "7log b=3
\n" ); document.write( "Dividing by 7,we get
\n" ); document.write( "log(b)=(3/7)
\n" ); document.write( "(here the base 10 is understood )
\n" ); document.write( "b= =[(10)^(3/7)]
\n" ); document.write( "--------------------------- \r
\n" ); document.write( "\n" ); document.write( "Note:Students tend to do the same as follows which is round about.\r
\n" ); document.write( "\n" ); document.write( "7log b=3
\n" ); document.write( "log[(b)^7] = 3 (here the base 10 is understood )
\n" ); document.write( "[using definition log(N) to base b is the power p to which the base has to be raised to give the number. that is N=(b)^ ]
\n" ); document.write( "[(b)^7] =[(10)^3] [using definition log(N) to base b is the power p to which the base has to be raised to give the number that is N=(b)^p and here N should be a strictly positive number]
\n" ); document.write( "Taking the seventh root on both the sides.
\n" ); document.write( "[(b)^7]^(1/7) =[(10)^3]^(1/7)
\n" ); document.write( "b= =[(10)^(3/7)] [using (a^m)^n = (a)^(mn)]\r
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\n" ); document.write( "\n" ); document.write( "3) 4ln(4d-2)=6
\n" ); document.write( "Dividing by 4
\n" ); document.write( "log(4d-2) = 6/4 =3/2 (cancelling 2 in the nr and in the dr)
\n" ); document.write( "log(4d-2)=(3/2)
\n" ); document.write( "implies (4d-2) = [(10)^(3/2)]
\n" ); document.write( "4d = [(10)^(3/2)]+2
\n" ); document.write( "Dividing by 4
\n" ); document.write( "d = (1/4)[(10)^(3/2)]+(1/2)\r
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