document.write( "Question 1061338: Solve the exponential equation:\r
\n" ); document.write( "\n" ); document.write( "8^x - 3(8^-x) = 2\r
\n" ); document.write( "\n" ); document.write( "My answer key says it's x = log(3)/log(8) but I have no idea how to get there
\n" ); document.write( "

Algebra.Com's Answer #676128 by MathTherapy(10556)\"\" \"About 
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\n" ); document.write( "Solve the exponential equation:\r
\n" ); document.write( "\n" ); document.write( "8^x - 3(8^-x) = 2\r
\n" ); document.write( "\n" ); document.write( "My answer key says it's x = log(3)/log(8) but I have no idea how to get there
\n" ); document.write( "
\"8%5Ex+-+3%288%5E%28-+x%29%29+=+2\" =====> \"8%5Ex+-+3%281%2F8%5Ex%29+=+2\" =====> \"8%5Ex+-+3%2F8%5Ex+=+2\" =====> \"8%5Ex+-+3%2F8%5Ex+-+2+=+0\"
\n" ); document.write( "\"8%5E%282x%29+-+3+-+2%288%5Ex%29+=+0\" ------- Multiplying by LCD, \"8%5Ex\"
\n" ); document.write( "\"8%5E%282x%29+-+2%288%5Ex%29+-+3+=+0\"
\n" ); document.write( "Let a = \"8%5Ex\"
\n" ); document.write( "Then, \"8%5E%282x%29+-+2%288%5Ex%29+-+3+=+0\" becomes: \"a%5E2+-+2a+-+3+=+0\"
\n" ); document.write( "(a - 3)(a + 1) = 0
\n" ); document.write( "a - 3 = 0 OR a + 1 = 0
\n" ); document.write( "a = 3 OR a = - 1
\n" ); document.write( "Replacing \"a\" with \"8%5Ex\"
\n" ); document.write( "\"8%5Ex+=+3\" OR \"8%5Ex+=+-+1\"
\n" ); document.write( " ------ Converting \"matrix%281%2C6%2C+8%5Ex%2C+%22=%22%2C+3%2C+to%2C+LOGARITHMIC%2C+form%29\"\r
\n" ); document.write( "\n" ); document.write( "\"matrix%281%2C3%2C+x%2C+%22=%22%2C+log+%288%2C+-+1%29%29\" ------ Converting \"matrix%281%2C6%2C+8%5Ex%2C+%22=%22%2C+-+1%2C+to%2C+LOGARITHMIC%2C+form%29\", but IGNORE this as LOG VALUE CANNOT be < 0 (negative) \n" ); document.write( "
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