document.write( "Question 79204: Thanks in advance - this is the last question on my homework and I can't figure it out. Solve for x
\n" ); document.write( "10^(2x-1)= e^(4x-3) \n" ); document.write( "

Algebra.Com's Answer #56846 by funmath(2933) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve for x
\n" ); document.write( "10^(2x-1)= e^(4x-3)
\n" ); document.write( " $\"ln%2810%5E%282x-1%29%29=ln%28e%5E%284x-3%29%29\"$
\n" ); document.write( "you can either take the common log, or the natural log of both sides. I chose natural log so that I didn't have to deal with e as a number.
\n" ); document.write( " $\"%282x-1%29ln%2810%29=%284x-3%29ln%28e%29\"$ ln(e)=1
\n" ); document.write( " $\"%282x-1%29ln%2810%29=4x-3\"$ distribute ln(10)
\n" ); document.write( " $\"2xln%2810%29-ln%2810%29=4x-3\"$ Get x's to one side of = sign.
\n" ); document.write( " $\"2xln%2810%29-4x-ln%2810%29=4x-4x-3\"$ get things without x's to the other side.
\n" ); document.write( " $\"2xln%2810%29-4x-ln%2810%29%2Bln%2810%29=ln%2810%29-3\"$
\n" ); document.write( " $\"2xln%2810%29-4x=ln%2810%29-3\"$ factor out the x's
\n" ); document.write( " $\"x%282ln%2810%29-4%29=ln%2810%29-3\"$ divide by the coefficient of x
\n" ); document.write( " $\"x%282ln%2810%29-4%29%2F%282ln%2810%29-4%29=%28ln%2810%29-3%29%2F%282ln%2810%29-4%29\"$
\n" ); document.write( " $\"x=%28ln%2810%29-3%29%2F%282ln%2810%29-4%29\"$ Put it in your calculator.
\n" ); document.write( " $\"x=-1.15243\"$
\n" ); document.write( "Happy Calculating!!!!
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