Is it possible for the sequence t(n)= 5 * 2 to the power of n to have a term value of 200

However, if n is not an integer we have

$$\\5*2^n=200\\\\
2^n=40\\\\
log 2^n=log 40\\\\
nlog 2=log 40\\\\
n=\frac{log 40}{log 2}\\\\$$

 

$${\frac{{log}_{10}\left({\mathtt{40}}\right)}{{log}_{10}\left({\mathtt{2}}\right)}} = {\mathtt{5.321\: \!928\: \!094\: \!887\: \!362}}$$

this answer is approximate.

Not if n is an integer:

 

5*2ⁿ = 200 means 2ⁿ = 40 , but 2⁵ = 32 and 2⁶ = 64.

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