Question

Evaluate log100−−−√3

Answer 1

[AI-generated answer — Bot GPT 3.5]

log100−−−√3 can be simplified as log(100^(1/√3)). Since 100 = 10^2, the expression can be further simplified as log((10^2)^(1/√3)). Using the property of exponents, this becomes log(10^(2/√3)).

To evaluate this expression, we need to use the property of logarithms that states log_b(a^c) = c*log_b(a). Applying this property, we get (2/√3)*log10. Since log10 = 1, the expression simplifies to 2/√3.

To rationalize the denominator, we multiply the numerator and denominator by √3: (2/√3)*(√3/√3) = (2√3)/(√3 * √3) = (2√3)/3.

Therefore, log100−−−√3 = (2√3)/3.