Can someone help me?
And for this problem, can you check if I solved it right:
Thank you
mean or and
You can write this as
.
Squaring both sides, , . By the "rational root theorem" the only possible rational roots are x= 1, x= -1, x= 2, x= -2, x= 4, and x= -4. Try those to see if any are actually roots.
Almost trivial: . Assuming that "log" here means common logarithm, . Solve that quadratic equation.[*]
Similar to the first one isn't it? means so and .[*]
so .
Yes, that is correct.And for this problem, can you check if I solved it right:
[/quote]Thank you [/QUOTE]
Note that 16 = 4^2. Apply the change-of-base formula to log_16(x) to convert and get:
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Note that log_16(4) = 1/2, so:
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Then:
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Solve the rational equation.
A straight-forward application of log rules and the definition of the common log leads to:
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Equate the arguments, and solve the resulting quadratic equation.
Note that the change-of-base formula says that log_{x^2}(9) = log_x(9) / log_x(x^2}, and log_x(x^2) obviously equals 2. Then:
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Equate the arguments, and simplify to solve.
Looks good to me! :wink: