solve for x exponent problems: 9*2^x=6^x & 18^2x * 3^-2x = 6
- Thread starter Mcar
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Otis
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Hi there. We don't do homework, but we'll help you to finish yours.
Have you memorized the properties of exponents? These three are useful:
(a*b)^x = a^x * b^x
(a/b)^x = a^x / b^x
a^(-x) = 1/a^x
Hint: Rewrite the 6 in factored form (2*3), then apply the first property above.
Apply the last property above, to get rid of that negative exponent.
Then (on the left-hand side), you'll have a ratio with the same exponent in the top and in the bottom. That form is just like the right-hand side of the second property above, so you may divide the bases as shown on the left-hand side of the property.
Show how far you get, if you need more guidance. :cool:
Have you memorized the properties of exponents? These three are useful:
(a*b)^x = a^x * b^x
(a/b)^x = a^x / b^x
a^(-x) = 1/a^x
Hint: Rewrite the 6 in factored form (2*3), then apply the first property above.
Apply the last property above, to get rid of that negative exponent.
Then (on the left-hand side), you'll have a ratio with the same exponent in the top and in the bottom. That form is just like the right-hand side of the second property above, so you may divide the bases as shown on the left-hand side of the property.
Show how far you get, if you need more guidance. :cool:
Last edited:
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Does the above mean the following?
. . . . .\(\displaystyle 9\, \cdot\, 2^x\, =\, 6^x\)
Does the above mean the following?
. . . . .\(\displaystyle 18^{2x}\, \cdot\, 3^{-2x}\, =\, 6\)
You already have loads of worked examples in your textbook and in your class notes, as well as whatever online lessons you've studied, so two more worked examples aren't likely to make much difference at this point. Now is the time to try stuff, and see what happens.
Please reply with a clear listing of your thoughts and efforts so far, so we can see where you're getting stuck and provide specific helps. Thank you!
