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Can You Solve For 'n'? | Math Olympiad Questions | A Beautiful Exponential Problem | Algebra problem
Can You Solve For 'n'? | Math Olympiad Questions | A Beautiful Exponential Problem | Algebra problem
Can You Solve For 'n'? | Math Olympiad Questions | A Beautiful Exponential Problem | Algebra problem
Can You Solve For 'n'? | Math Olympiad Questions | A Beautiful Exponential Problem | Algebra problem
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[@kanguru_]

x=2 by inspection.

[@roger7341]

Nice trick if you recognize that (√3-√2)=1/(√3+√2). Substitute y=(√3+√2)^x into the given equation: y+1/y-10=0 and rearrange to y^2-10y+1=0, which has roots y=(10±4√6)/2=5±2√6. Thus x=ln(5±2√6)/ln(√3+√2)=±2