document.write( "Question 167591: Will someone please help me on these two problems. I was absent and have a test on them later today.
\n" ); document.write( "1. Use log5 2~0.4307 and log5 3~0.6826 to approximate the value of log5 12.
\n" ); document.write( "2. Express log6 19 in terms of common logarithms. Then approximate its value to four decimal places.
\n" ); document.write( "I must show my work. Can you please help me through these
\n" ); document.write( "Thanks \n" ); document.write( "
Algebra.Com's Answer #123588 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
1. Use log5 2~0.4307 and log5 3~0.6826 to approximate the value of log5 12.
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\n" ); document.write( "So, instead of
\n" ); document.write( "log5(12)
\n" ); document.write( "we can write:
\n" ); document.write( "log5(2*2*3)
\n" ); document.write( "Applying log rule below:
\n" ); document.write( "logb(mn) = logb(m) + logb(n)
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\n" ); document.write( "we get:
\n" ); document.write( "log5(2*2*3) = log5(2) + log5(2) + log5(3)
\n" ); document.write( "Now, we can substitute in the provided values:
\n" ); document.write( "log5(2*2*3) = 0.4307 + 0.4307 + 0.6826
\n" ); document.write( "log5(2*2*3) = 1.544
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\n" ); document.write( "2. Express log6 19 in terms of common logarithms. Then approximate its value to four decimal places.
\n" ); document.write( ".
\n" ); document.write( "For this, we'll need to apply the change-of-base formula:
\n" ); document.write( "logb(x) = log(x)/log(b)
\n" ); document.write( "where \"log\" without a base indicates base 10.
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\n" ); document.write( "So, now we can rewrite:
\n" ); document.write( "log6(19) = log(19)/log(6)
\n" ); document.write( "At this point, you'll need your calculator:
\n" ); document.write( "log6(19) = 1.27875/0.77815
\n" ); document.write( "log6(19) = 1.6433\r
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