Question 150970
I'm assuming that the "x" is really a multiplication symbol. 


{{{3*5^(2t-1)=75}}} Start with the given equation.



{{{5^(2t-1)=25}}} Divide both sides by 3.



{{{5^(2t-1)=5^2}}} Rewrite 25 as {{{5^2}}}



{{{2t-1=2}}} Since the bases are equal, this means that the exponents are equal.



{{{2t=2+1}}} Add {{{1}}} to both sides.



{{{2t=3}}} Combine like terms on the right side.



{{{t=(3)/(2)}}} Divide both sides by {{{2}}} to isolate {{{t}}}.



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Answer:


So the answer is {{{t=3/2}}} 



Which approximates to {{{t=1.5}}}