Evaluate: log3 9 + 3log2 8 − 10^2log 3

Answer 1

Since all bases are different, it's probably easier to convert to integers. Remember to log of a number is an exponent therefore,

log₃ 9 + 3log₂ 8 - 10^{2log 3}

^{Rewrite for clarity}

log₃ 9 + 3(log₂ 8) - (10^log₁₀ ³ )²

= 2 + 3(3) - (3)²

^{= 2}

^{Study properties of exponents and conversions fro logarithmic to exponential forms and you'll be set!}