document.write( "Question 696666: Solve for x: 3^2x=27^x+1
\n" ); document.write( "2. Solve for x: 25^x-1=125^x
\n" ); document.write( "3.Solve for x: 16^x-2=(1/8)^x
\n" ); document.write( "Please help me.We didn't even learn any of this is class and I don't know to how solve it or start it. Please help. Step by step procedure will be helpful. Thanks in advance! \n" ); document.write( "

Algebra.Com's Answer #429217 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve for x:
\n" ); document.write( " $\"3%5E%28%282x%29%29+=++27%5E%28%28x+%2B+1%29%29\"$
\n" ); document.write( "Note that we can write 27 as a power of 3, 27 = 3^3, so we have
\n" ); document.write( " $\"3%5E%28%282x%29%29+=++3%5E%283%28x+%2B+1%29%29\"$
\n" ); document.write( "both exponents are powers of 3, therefore we can write it
\n" ); document.write( "2x = 3(x+1)
\n" ); document.write( "2x = 3x + 3
\n" ); document.write( "-3 - 3x - 2x
\n" ); document.write( "-3 = x
\n" ); document.write( ":
\n" ); document.write( "You can check this on a calc
\n" ); document.write( "enter: 3^(2*-3) look at the result
\n" ); document.write( "enter: 27(-3+1) see that the result is the same
\n" ); document.write( ";
\n" ); document.write( ":
\n" ); document.write( "2. Solve for x:
\n" ); document.write( " $\"25%5E%28%28x-1%29%29=125%5Ex\"$
\n" ); document.write( "The same situation here; 25 = 5^2 and 125 = 5^3, so we can write it
\n" ); document.write( " $\"5%5E%282%28x-1%29%29=5%5E%28%283x%29%29\"$
\n" ); document.write( "Both exponents are the power of the same number (5) therefore
\n" ); document.write( "2(x-1) = 3x
\n" ); document.write( "2x - 2 = 3x
\n" ); document.write( "-2 = 3x - 2x
\n" ); document.write( "-2 = x
\n" ); document.write( ":
\n" ); document.write( "Check this on your calc
\n" ); document.write( "enter 25^(-2-1)
\n" ); document.write( "enter 125^(-2)
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "3.Solve for x: 16^x-2=(1/8)^x
\n" ); document.write( " $\"16%5E%28%28x-2%29%29=%281%2F8%29%5Ex\"$
\n" ); document.write( "we can write both as powers of 2, 2^4 = 16 and recall that 1/8 = 2^-3
\n" ); document.write( " $\"2%5E%284%28x-2%29%29\"$ = $\"2%5E%28%28-3x%29%29\"$
\n" ); document.write( "so we have
\n" ); document.write( "4(x-2) = -3x
\n" ); document.write( "4x - 8 = -3x
\n" ); document.write( "4x + 3x = + 8
\n" ); document.write( "7x = +8
\n" ); document.write( "x = 8/7
\n" ); document.write( ":
\n" ); document.write( "Check this
\n" ); document.write( "Enter: 16^((8/7)-2)
\n" ); document.write( "Enter: (1/8)^(8/7)
\n" ); document.write( " \n" ); document.write( "

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