i really need to know how to solve these equations. thanks!

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- Jan 12th 2010, 03:04 AMfishlord40logarithm/exponential equations
i really need to know how to solve these equations. thanks!

http://uploadpic.org/thumb-38610.jpg - Jan 12th 2010, 03:52 AMtonio

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

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

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

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

Tonio