Log[2,65^101]=Log[2,1.19677265435936523306697061008844595216875076047476380412892350218210371675034710110019059670045148702617743840309261226642554018932731196136801743304996144204565628864850066945087397917271469158502290037902267351495422972809927640213263311022179210777110235878476261713286260715512346296228729355809204331953969381189138372868792929884027176059624888933097619531656360169878919165635879174145849177127325380092091751385947493182122573867203591393456535269835771605697632270612450222562872035496584999815505313956003807991807327209204088716906381122033679207810157583448396056979845525347627699375152587890625]+608

asked by guest
on Apr 06, 2025 at 6:02 pm



You asked:

Investigate the equation: log⁡2(65101)=log⁡2(1.19677265435936523306697061008844595216875076047476380412892350218210371675034710110019059670045148702617743840309261226642554018932731196136801743304996144204565628864850066945087397917271469158502290037902267351495422972809927640213263311022179210777110235878476261713286260715512346296228729355809204331953969381189138372868792929884027176059624888933097619531656360169878919165635879174145849177127325380092091751385947493182122573867203591393456535269835771605697632270612450222562872035496584999815505313956003807991807327209204088716906381122033679207810157583448396056979845525347627699375152587890625)+608\log_{2}\left( {65}^{101} \right) = \log_{2}\left( 1.19677265435936523306697061008844595216875076047476380412892350218210371675034710110019059670045148702617743840309261226642554018932731196136801743304996144204565628864850066945087397917271469158502290037902267351495422972809927640213263311022179210777110235878476261713286260715512346296228729355809204331953969381189138372868792929884027176059624888933097619531656360169878919165635879174145849177127325380092091751385947493182122573867203591393456535269835771605697632270612450222562872035496584999815505313956003807991807327209204088716906381122033679207810157583448396056979845525347627699375152587890625 \right) + 608.

MathBot Answer:

This equation has no unknown quantities, so it is either true or false.

This equation is true because the left-hand side is equal to the right-hand side.

The left-hand side of the equation is:

log⁡2(65101)=log⁡(1271302850988855649955877740540614892475208187760352651691755289585430714023709374227697793688402207534181186063394457937494576689321514086626098427590392248021089471876621246337890625)log⁡(2)\log_{2}\left( {65}^{101} \right) = \frac{\log{\left(1271302850988855649955877740540614892475208187760352651691755289585430714023709374227697793688402207534181186063394457937494576689321514086626098427590392248021089471876621246337890625 \right)}}{\log{\left(2 \right)}}

The right-hand side of the equation is:

log⁡2(1.19677265435936523306697061008844595216875076047476380412892350218210371675034710110019059670045148702617743840309261226642554018932731196136801743304996144204565628864850066945087397917271469158502290037902267351495422972809927640213263311022179210777110235878476261713286260715512346296228729355809204331953969381189138372868792929884027176059624888933097619531656360169878919165635879174145849177127325380092091751385947493182122573867203591393456535269835771605697632270612450222562872035496584999815505313956003807991807327209204088716906381122033679207810157583448396056979845525347627699375152587890625)+608=log⁡(1271302850988855649955877740540614892475208187760352651691755289585430714023709374227697793688402207534181186063394457937494576689321514086626098427590392248021089471876621246337890625)log⁡(2)\log_{2}\left( 1.19677265435936523306697061008844595216875076047476380412892350218210371675034710110019059670045148702617743840309261226642554018932731196136801743304996144204565628864850066945087397917271469158502290037902267351495422972809927640213263311022179210777110235878476261713286260715512346296228729355809204331953969381189138372868792929884027176059624888933097619531656360169878919165635879174145849177127325380092091751385947493182122573867203591393456535269835771605697632270612450222562872035496584999815505313956003807991807327209204088716906381122033679207810157583448396056979845525347627699375152587890625 \right) + 608 = \frac{\log{\left(1271302850988855649955877740540614892475208187760352651691755289585430714023709374227697793688402207534181186063394457937494576689321514086626098427590392248021089471876621246337890625 \right)}}{\log{\left(2 \right)}}

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