Hello everyone! My question is twofold. Firstly, how do I solve for term numbers in a geometric sequence and secondly, how do I algebraically solve for variables that are exponents?(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Given the following geometric sequences, determine the number of terms, n.

t_{1}=5

r (common ratio)=3

t_{n}=135

2. Relevant equations

t_{n}=t_{1}r^{n-1}

where t_{1}is the first term

n is the number of terms

r is the common ratio

t_{n}is the general term

3. The attempt at a solution

I substituted in all known values yielding 135=(5)(3)^{n-1}, which I simplified to 27=(3)^{n-1}, leaving me stuck at the exponent variable. From here, how do I algebraically solve for the variable? Thanks!

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# Homework Help: Geometric sequences; solving algebraically for exponents

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