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Answer :
We have been asked to find the solution of
[tex] {Log_{(2x-3)}}^{125}=3\\
\\
\text{we can re-write after Removing logarithm as below}\\
\\
(2x-3)^3=125\\
\\
(2x-3)^3=5^3\\
\\
\text{Now take cubed root on both the sides we get}\\
\\
2x-3=5\\
\\
\text{Add 3 on both the sides we get}\\
\\
2x=8\\
\\
\text{Divide both the sides by 2 we get}\\
\\
x=4
[/tex]
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Rewritten by : Barada
The correct solution is x = 4, option D.
The solution of the equation log2x - 3125 = 3 can be found by isolating the term with the logarithm. First, let's assume the typos are actually meaning to state log(2x) = 3. To solve for x, we would use the property that if [tex]log_b[/tex](a) = c, then a = bc, where b is the base of the logarithm, a is the argument, and c is the log value.
Applying this property to the original equation, we would rewrite it as:
2x = 23
Since 23 is equal to 8:
2x = 8
Now we can divide both sides by 2 to solve for x:
x = 4
Therefore, the solution of the given logarithmic equation is x = 4, which corresponds to option d).
