Solve each equation . CLICK !

Question

whpalmer4 · Answer

I clicked, but no equations appeared.

anonymous · Answer

oh sorry. give me 30 secs.

anonymous · Answer

$$\log _{x}32=-5$$

anonymous · Answer

@whpalmer4

whpalmer4 · Answer

Okay, the log base x of 32 is the number that x needs to be raised to to give you 32.

anonymous · Answer

okay ? @whpalmer4

whpalmer4 · Answer

Nuts, lost the response I was writing :-(

If the log base x of 32 = -5, that means that $x^{-5} = 32$

whpalmer4 · Answer

And by the properties of exponents, $$x^{-5} = \frac{1}{x^5}$$

we could solve this by figuring out which number raised to the 5th power = 32, then take its reciprocal.  What is the value of a if a*a*a*a*a = 32?  1/a will be our answer.

anonymous · Answer

sorry  for the delay. but 2^5=32?

anonymous · Answer

1/2 is the answer?

whpalmer4 · Answer

Yes. 1/2*1/2*1/2*1/2*1/2 = 1/32

anonymous · Answer

can you help me with the next one?

whpalmer4 · Answer

And by the change of base formula, 
$$\log_b a = \frac{\log b}{\log a} = -5 = \frac{\log 32}{\log x}$$$$-5 \log x = \log 32$$$$\log x = \log 32/-5$$$$x = e^{\log 32/-5} = 1/2$$

whpalmer4 · Answer

Post new questions in separate questions. Better for me, better for you.