Solve for x:
16^3x-2=(1/32)^2x-16
How to start this?
Thanks in advance.
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Solve for x:
16^3x-2=(1/32)^2x-16
How to start this?
Thanks in advance.
A good place to start would be to restate the problem using bracketing symbols to let us know what the exponents actually are.
Hello, maiden129!
Quote:
Solve for x: 16^3x-2=(1/32)^2x-16
If that equation is: .$\displaystyle 16^{3x} -2 \:=\:\left(\tfrac{1}{32}\right)^{2x} - 16$
we have: .$\displaystyle (2^4)^{3x} \:=\:(2^{-5})^{2x} - 14 \quad\Rightarrow\quad 2^{12x} \:=\:2^{-10x} - 14 $
. . . . . . . . $\displaystyle 2^{12x} + 14 - 2^{-10x} \:=\:0$
Multiply by $\displaystyle 2^{10x}\!\!:\;\;2^{22x} + 14\cdot 2^{10x} + 1 \;=\;0$
Good luck!
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If the equation is: .$\displaystyle 16^{3x-2} \:=\:\left(\tfrac{1}{32}\right)^{2x-16}$
we have: .$\displaystyle (2^4)^{3x-2} \:=\:(2^{-5})^{2x-16} \quad\Rightarrow\quad 2^{12x-8} \:=\:2^{-10x+80} $
Therefore: .$\displaystyle 12x - 8 \:=\:-10x + 80 \quad\Rightarrow\quad 22x \:=\:88 \quad\Rightarrow\quad x \:=\:4$
