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How do you solve #log_9 x = 1.5#?

Answer 1

Elijah Allen

#:. x=27#.

By Defn., #log_b a=m iff a=b^m#.

# :. log_9 x=1.5 rArr 9^(1.5)=x#

#:. x=(3^2)^(1.5)#

#:. x=3^(2xx1.5)#.

#;. x=3^3#.

#:. x=27#.

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Answer 2

Sophie Adams

To solve ( \log_9 x = 1.5 ), we first rewrite the equation in exponential form.

( \log_9 x = 1.5 ) can be rewritten as ( 9^{1.5} = x ).

Now, we calculate ( 9^{1.5} ) to find the value of ( x ).

( 9^{1.5} = \sqrt{9^3} = \sqrt{729} = 27 ).

So, the solution to the equation ( \log_9 x = 1.5 ) is ( x = 27 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.