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# Logs question watch

1. "Grandpa gives Simon £5 on his first birthday and increases this amount by 10% each year.

Simon gets a present of over £50 on his nth birthday. Show that:

n > [1 / (log_10_1.1) ] +1." ***the _10_ means to base 10***

What I've worked out:
a=5,
r=1.1 (so multiply by 1.1 each time)
n > 5 x 1.1^n
I don't know where to go from there. I'm confused about why the logarithm is to base 10. Maybe just point me in the right direction. Thank you in advance!
2. (Original post by JustJusty)
"Grandpa gives Simon £5 on his first birthday and increases this amount by 10% each year.

Simon gets a present of over £50 on his nth birthday. Show that:

n > [1 / (log_10_1.1) ] +1." ***the _10_ means to base 10***

What I've worked out:
a=5,
r=1.1 (so multiply by 1.1 each time)
n > 5 x 1.1^n
I don't know where to go from there. I'm confused about why the logarithm is to base 10. Maybe just point me in the right direction. Thank you in advance!
What's the nth term of that geometric series? Hint: nth term is: - you know this is greater than 50. So: Now divide and take logarithms.
3. (Original post by Zacken)
What's the nth term of that geometric series? Hint: nth term is: - you know this is greater than 50. So: Now divide and take logarithms.
Thank you! This helped a lot.
4. (Original post by JustJusty)
Thank you! This helped a lot.
My pleasure.

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