Solve 5^(x+5)=9^x
a)x≈–3.63
b)x≈–0.28
c)x≈0.07
d)x≈13.69

Question

Solve 5^(x+5)=9^x
a)x≈–3.63
b)x≈–0.28
c)x≈0.07
d)x≈13.69

anonymous · Answer

i know it is not A

tkhunny · Answer

Have you considered the logarithm function?

anonymous · Answer

could you please state the function, i'm a litle rusty at algebra

tkhunny · Answer

Why are you given this problem if you've no logarithm?  Is this a placement exam?  If it is a placement exam, you should get this problem wrong so that the examiner will know that you need more work in this area.

anonymous · Answer

no this is review packet for finals and i forgot how to do this type of problem

tkhunny · Answer

If you say so.  One for free.

$5^{x+5}=9^{x}$

Introduce the logarithm

$\log\left(5^{x+5}\right)=\log\left(9^{x}\right)$

logarithm properties

$(x+5)\cdot \log(5)=x\cdot \log(9)$

Distributive property

$x\cdot \log(5) + 5\cdot \log(5)=x\cdot \log(9)$

Can you solve this for 'x'?

anonymous · Answer

so
 $$.698970004336019(x+5)=.9542509439325(x)$$

anonymous · Answer

so the answer is d) 13.69

tkhunny · Answer

That's kind of a mess, but you did find the right answer.  I would suggest you review this section quite a bit more and brush up on your logarithms and your basic algebra.  you switched to your calculator WAY too quickly.