document.write( "Question 1200017: Solve the following exponential equations
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Algebra.Com's Answer #834023 by ikleyn(52787)\"\" \"About 
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\n" ); document.write( "Solve the following exponential equations
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document.write( "(a)  \"3%5Ex\" = \"5%2A2%5Ex\".\r\n" );
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document.write( "     Take logarithm base 10 of both sides. Use properties of logarithms.  You will get\r\n" );
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document.write( "     x*log(3) = log(5) + x*log(2)\r\n" );
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document.write( "     x*log(3) - x*log(2) = log(5)\r\n" );
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document.write( "     x*(log(3) - log(2)) = log(5)\r\n" );
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document.write( "     x = \"log%28%285%29%29%2F%28log%28%283%29%29-log%28%282%29%29%29\" = 3.969  (rounded).    ANSWER\r\n" );
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document.write( "(b)  \"9%5E%28x-1%29%2A3%5Ex\" = \"27\"\r\n" );
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document.write( "     It is the same as\r\n" );
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document.write( "     \"%283%5E2%29%5E%28x-1%29%2A3%5Ex\" = \"27\"\r\n" );
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document.write( "     \"3%5E%282%28x-1%29%29%2A3%5Ex\" = \"3%5E3\"\r\n" );
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document.write( "     \"3%5E%282x-2%2Bx%29\" = \"3%5E3\"\r\n" );
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document.write( "     \"3%5E%283x-2%29\" = \"3%5E3\"\r\n" );
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document.write( "     The base is 3 in both sides of the equation - hence, the degrees are identical\r\n" );
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document.write( "     3x-2 = 3\r\n" );
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document.write( "     3x = 3+2 = 5\r\n" );
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document.write( "      x       = \"5%2F3\".    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "On logarithms and their properties,  see these introductory lessons\r
\n" ); document.write( "\n" ); document.write( "    - WHAT IS the logarithm \r
\n" ); document.write( "\n" ); document.write( "    - Properties of the logarithm \r
\n" ); document.write( "\n" ); document.write( "    - Change of Base Formula for logarithms \r
\n" ); document.write( "\n" ); document.write( "    - Evaluate logarithms without using a calculator \r
\n" ); document.write( "\n" ); document.write( "    - Simplifying expressions with logarithms \r
\n" ); document.write( "\n" ); document.write( "    - Solving logarithmic equations \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Logarithms\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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