# logarithm/exponential equations

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• Jan 12th 2010, 04:04 AM
fishlord40
logarithm/exponential equations
i really need to know how to solve these equations. thanks!

http://uploadpic.org/thumb-38610.jpg
• Jan 12th 2010, 04:52 AM
tonio
Quote:

Originally Posted by fishlord40
i really need to know how to solve these equations. thanks!

http://uploadpic.org/thumb-38610.jpg

Assuming $\log a=\log_{10}a$ , and assuming you made a typo and meant $\log\log x$ in the first exer., then

$\log\log x=3\Longrightarrow 10^3=\log x \Longrightarrow 10^{10^3}=x$

$x^{\log_2x}=32x^4\Longrightarrow \log_2\left(x^{\log_2x}\right)=\log_2\left(32x^4\r ight)\Longrightarrow$ $\log_xx\cdot\log_2x=5+4\log_2x$ ...you finish the argument.

Of course, you must know VERY WELL the definition and properties of logarithms to prove the above.

Tonio