logarithm/exponential equations

**fishlord40** · January 12th 2010, 03:04 AM

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

**tonio** · January 12th 2010, 03:52 AM

Originally Posted by fishlord40

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

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

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