document.write( "Question 702490: Solve the equation of loga 16= -4 \n" ); document.write( "
Algebra.Com's Answer #433033 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hi, there--\r\n" );
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document.write( "The Problem--\r\n" );
document.write( "Solve the equation log[a] 16 = -4\r\n" );
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document.write( "A Solution--\r\n" );
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document.write( "Often it's helpful with logarithm problems to translate them to exponent language.\r\n" );
document.write( "We have log base a of 16 is -4. In exponent language we have the number a raised to the -4 power to give 16. \r\n" );
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document.write( "a^(-4) = 16\r\n" );
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document.write( "Rewrite this without the negative exponent.\r\n" );
document.write( "1/(a^4) = 16\r\n" );
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document.write( "Solve for a.\r\n" );
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document.write( "a^4 = 1/16\r\n" );
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document.write( "a = 4th root of 1/16. In other words, what number can I multiply by itself 4 times to give \r\n" );
document.write( "1/16?\r\n" );
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document.write( "(1/2)^4 = (1/2)*(1/2)*(1/2)*(1/2) = 1/16\r\n" );
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document.write( "a = 1/2\r\n" );
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document.write( "Let's check our answer. First in exponent language, then in logarithm language. Substitute\r\n" );
document.write( "1/2 for a.\r\n" );
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document.write( "a^(-4) = 16\r\n" );
document.write( "(1/2)^(-4) = 16\r\n" );
document.write( "1/((1/2)^4) = 16\r\n" );
document.write( "1/(1/16) = 16\r\n" );
document.write( "16 = 16 \r\n" );
document.write( "Check!\r\n" );
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document.write( "log[a] 16 = -4\r\n" );
document.write( "log[1/2] 16 = -4\r\n" );
document.write( "-4 = -4 \r\n" );
document.write( "Check!\r\n" );
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document.write( "Hope this helps! Contact me if you still have questions; I'll be happy to answer.\r\n" );
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document.write( "Mrs.Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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