Answer:
[tex]x\:>\:6.64386[/tex]
Step-by-step explanation:
We want to find the value of [tex]x[/tex] for which [tex]2^x\:>\:100[/tex]
We take logarithm to base 2 of both sides.
[tex]\implies \log_22^x\:>\:\log_2100[/tex]
[tex]x\log_22\:>\:\log_2100[/tex]
Recall that: [tex]\log_aa=1[/tex]
[tex]x(1)\:>\:\log_2100[/tex]
[tex]x\:>\:6.64386[/tex]
