document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=262519>Question 262519</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation 3log[base5]x - log[base5]4 = log[base5]16.\r<BR>\n" );
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document.write( "Solve the equation 1/3log[base7]64+1/2log[base7]121=log[base7]x\r<BR>\n" );
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document.write( "Find log[base3]25 given that log[base3]5 = 1.465 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193388 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=193388\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we are given three separate problems. Lets take one at a time:<BR>\n" );
document.write( "Problem #1: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3log%285%2Cx%29+-+log%285%2C4%29+=+log%285%2C16%29 ALIGN=MIDDLE  ALT=\"3log%285%2Cx%29+-+log%285%2C4%29+=+log%285%2C16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "step 1- use the power rule to bring all coefficients up as exponents. We get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2Cx%5E3%29+-+log%285%2C4%29+=+log%285%2C16%29 ALIGN=MIDDLE  ALT=\"log%285%2Cx%5E3%29+-+log%285%2C4%29+=+log%285%2C16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "step 2 - using laws of logs if we see log subtraction, that means division, so we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2Cx%5E3%2F4%29+=+log%285%2C16%29 ALIGN=MIDDLE  ALT=\"log%285%2Cx%5E3%2F4%29+=+log%285%2C16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "step 3 - since both logs are base 5, we can eliminate then and set the rest equal. We get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2F4+=+16 ALIGN=MIDDLE  ALT=\"x%5E3%2F4+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 4 - multiply by 4 to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+=+64 ALIGN=MIDDLE  ALT=\"x%5E3+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 5 - take a cube root to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------<BR>\n" );
document.write( "problem #2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29log%287%2C64%29%2B%281%2F2%29log%287%2C121%29=log%287%2Cx%29 ALIGN=MIDDLE  ALT=\"%281%2F3%29log%287%2C64%29%2B%281%2F2%29log%287%2C121%29=log%287%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 1- use the power rule to bring all coefficients up as exponents. We get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%2C64%5E%281%2F3%29%29%2Blog%287%2C121%5E%281%2F2%29%29=log%287%2Cx%29 ALIGN=MIDDLE  ALT=\"log%287%2C64%5E%281%2F3%29%29%2Blog%287%2C121%5E%281%2F2%29%29=log%287%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 2 - using laws of logs if we see log addition, that means multiplication<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%287%2C64%5E%281%2F3%29%2A121%5E%281%2F2%29%29+=+log%287%2Cx%29 ALIGN=MIDDLE  ALT=\"log%287%2C64%5E%281%2F3%29%2A121%5E%281%2F2%29%29+=+log%287%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 3 - since both logs are base 7, we can eliminate then and set the rest equal. We get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A11+=+x ALIGN=MIDDLE  ALT=\"4%2A11+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+44 ALIGN=MIDDLE  ALT=\"x+=+44\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------<BR>\n" );
document.write( "problem #3:<BR>\n" );
document.write( "Find <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C25%29 ALIGN=MIDDLE  ALT=\"log%283%2C25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C5%29+=+1.465 ALIGN=MIDDLE  ALT=\"log%283%2C5%29+=+1.465\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 1 - rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C25%29 ALIGN=MIDDLE  ALT=\"log%283%2C25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C5%5E2%29 ALIGN=MIDDLE  ALT=\"log%283%2C5%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and using power rules of logs, bring the 2 out front to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2log%283%2C5%29 ALIGN=MIDDLE  ALT=\"2log%283%2C5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 2 - by substitution, we get<BR>\n" );
document.write( "2*1.465 = 2.93 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );