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Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[8.2^{n-3}=42.5\] \[ln(8.2^{n-3})=ln(42.5)\]
\[(n-2)ln(8.2)=ln(42.5)\] \[n-2=\frac{ln(42.5)}{ln(8.2)}\]

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\[n=\frac{ln(42.5)}{ln(8.2)}+2\]
need the next one? works the same i think
step 1. take the log of both sides
yes
step 2 pull out the exponent as a multiplier
step 3 now that everything is on the ground floor use algebra. i will write it
\[2.1^{t-5}=9.2\]
frist one how u get (n-2)
because i made a typo. replace the 2 by a 3!
i typed it in wrong at the start. 2 should be 3. all other steps are the same
i will write the next one \[2.1^{t-5}=9.2\] step 1 take the log of both sides \[ln(2.1^{t-5})=ln(9.2)\]
step 2 pull the t - 5 out front as a multipier \[(t-5)ln(2.1)=ln(9.2)\]
ste 3 divide both sides by ln(2.1) we are trying to get t by itself \[t-5=\frac{ln(9.2)}{ln(2.1)}\]
step 4 add 5 to both sides \[t=\frac{ln(9.2)}{ln(2.1)}+5\]
done
u great ,thank
welcome!

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