Solve each equation using logarithms. Round to the nearest ten-thousandth.
1) 3^b= 17
2) 12^r= 13
3) 5x18^6x= 26
4) 11^n-8-5= 54
5) 16^n-7+5= 24

Question

Solve each equation using logarithms. Round to the nearest ten-thousandth. 
1) 3^b= 17 
2) 12^r= 13
3) 5x18^6x= 26
4) 11^n-8-5= 54
5) 16^n-7+5= 24

anonymous · Answer

I'll show the first one. You should be able to do the second one after that.

$$3^b = 17$$
Take the log of both sides (You can choose base 3, but you don't have to. I'm going to choose base 10)
$$Log(3^b) = Log(17)$$
Now, use your log rules and solve for b:
$$b Log(3) = Log(10)$$
$$b = \frac{Log(10)}{Log(3)}$$
Just throw that into a calculator :)


Can you do 2?

anonymous · Answer

Oh, for some reason I changed my 17 to a 10. Sorry about that.

$$b = \frac{Log(17)}{Log(3)}$$