document.write( "Question 947737: Use logarithms to solve the given equation. (Round the answer to four decimal places.) 7^−4x = 45 \n" ); document.write( "

Algebra.Com's Answer #578348 by Theo(13342) $\"\"$ $\"About$

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start with 7^(-4x) = 45
\n" ); document.write( "take the log of both sides of this equation to get:
\n" ); document.write( "log(7^(-4x)) = log(45)
\n" ); document.write( "this becomes -4x*log(7) = log(45)
\n" ); document.write( "divide both sides of this equation by log(7) to get:
\n" ); document.write( "-4x = log(45) / log(7)
\n" ); document.write( "divide both sides of this equation by -4 to get:
\n" ); document.write( "x = log(45) / (log(7) / -4
\n" ); document.write( "solve for x to get x = -.4890593859
\n" ); document.write( "confirm by replacing x in the original equation to get:
\n" ); document.write( "7^(-4*-.4890593859) = 45
\n" ); document.write( "simplify to get 45 = 45.
\n" ); document.write( "this confirms the solution is correct.
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