What is x if #log_3 (2x-1) = 2 + log_3 (x-4)#?

Answer 1

#x = 5#

We will use the following:

#log_3(2x-1) = 2 + log_3(x-4)#
#=> log_3(2x-1) - log_3(x-4) = 2#
#=>log_3((2x-1)/(x-4)) = 2#
#=> 3^(log_3((2x-1)/(x-4))) = 3^2#
#=> (2x-1)/(x-4) = 9#
#=> 2x - 1 = 9x - 36#
#=> -7x = -35#
#=> x = 5#
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Answer 2

I found: #x=5#

We can start writing it as: #log_3(2x-1)-log_3(x-4)=2# use the property of the logs: #logx-logy=log(x/y)# and write: #log_3((2x-1)/(x-4))=2# use the definition of log: #log_bx=a->x=b^a# to get: #(2x-1)/(x-4)=3^2# rearranging: #2x-1=9(x-4)# #2x-9x=-36+1# #7x=35# #x=35/7=5#
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Answer 3

To find the value of (x) in the equation (\log_3(2x - 1) = 2 + \log_3(x - 4)), you can use properties of logarithms.

First, apply the product rule of logarithms, which states that (\log_b(M) + \log_b(N) = \log_b(M \cdot N)).

Then, apply the power rule of logarithms, which states that (n \cdot \log_b(M) = \log_b(M^n)).

After combining the logarithms, solve for (x).

[ \begin{align*} \log_3(2x - 1) &= 2 + \log_3(x - 4) \ \log_3(2x - 1) &= \log_3(3^2) + \log_3(x - 4) \ \log_3(2x - 1) &= \log_3(9) + \log_3(x - 4) \ \log_3(2x - 1) &= \log_3(9(x - 4)) \ 2x - 1 &= 9(x - 4) \ 2x - 1 &= 9x - 36 \ -1 + 36 &= 9x - 2x \ 35 &= 7x \ x &= \frac{35}{7} \ x &= 5 \end{align*} ]

So, (x = 5).

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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.

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.

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.

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.

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