1000 = (〖1.01〗^(x)-1)/〖1.01〗^x
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1000 = (〖1.01〗^(x)-1)/〖1.01〗^x
by cross multiplication
1000*1.01^x = (〖1.01〗^(x)-1)
1000*1.01^x -1.01^(x) =-1
1.01^x(1-1000) =1
1.01^x(0.999) =1
1.01^x =1/0.999
Now take log of both sides
xln1.01=-ln0.999
x=-ln0.999/ln1.01
by cross multiplication
1000*1.01^x = (〖1.01〗^(x)-1)
1000*1.01^x -1.01^(x) =-1
1.01^x(1-1000) =1
1.01^x(0.999) =1
1.01^x =1/0.999
Now take log of both sides
xln1.01=-ln0.999
x=-ln0.999/ln1.01
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yes