Difficult logarithm question
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abhishekkgp
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View attachment 1637
Hello!
Attached is a math question that I couldn't solve during a test, I would really appreciate it if anyone can show me the method to solve it
Thanks in advance
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You were correct by multiplying by \(\displaystyle 5^{x}\).
\(\displaystyle 2\cdot 5^{2x+1}=5^{x}+3\)
\(\displaystyle 10\cdot 5^{2x}-5^{x}-3=0\)
Now, it is a quadratic by letting \(\displaystyle u=5^{x}\)
\(\displaystyle 10u^{2}-u-3=0\)
This factors. There is one extraneous solution....the negative one.
Can you finish now?.
You were correct by multiplying by \(\displaystyle 5^{x}\).
\(\displaystyle 2\cdot 5^{2x+1}=5^{x}+3\)
\(\displaystyle 10\cdot 5^{2x}-5^{x}-3=0\)
Now, it is a quadratic by letting \(\displaystyle u=5^{x}\)
\(\displaystyle 10u^{2}-u-3=0\)
This factors. There is one extraneous solution....the negative one.
Can you finish now?.