Solve the equation 5=40(1.3)^x for x using logs.

Question

allank · Answer

Hint: I would first divide both sides by 40.

anonymous · Answer

I tried i need to get a negative number but my answer keeps coming up positive i have no idea why

allank · Answer

Kindly show your working...

anonymous · Answer

divide both sides by 40 so do ln5/40=ln52/40 got the 52 from doing 40(1.3)... this was my lattest attempt

allank · Answer

Let's do it stepwise: Dividing by 40 will give you: 0.125=1.3^x
Now, introduce logs to both sides of the equation....

allank · Answer

What do we get? Note: Don't calculate yet, just show me what the log will do to the equation.

anonymous · Answer

so we get ln0.125=ln1.3^x or does the lnget rid of the ^in this step

allank · Answer

So far you're right. Now, modify the right side of the equals sign using the relationship:
ln a^b=b*ln a

anonymous · Answer

I actually just went ahead and calculated it using what you told me it seems i wasnt dividing both sides by 40 thatswhy my logs always came out positive when i divided them off in the end

anonymous · Answer

andi double checked with what you just said also

allank · Answer

Wonderful. Glad to be of help.

anonymous · Answer

Thank you very much

allank · Answer

You're welcome.