# Properties of Logarithms

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 What is log15(2^3) rewritten using the power property? d. 3log(15^2) What is log5(4 * 7) + log(5^2) written as a single log? d. log(5^56) What is 2log5(5x^3) + 1/3 log5 (x^2 + 6) written as a single logarithm? b. log5(25x^6)3√x^2 + 6 Which expression is equivalent to log3 (c/9)? c. log3 c – log3(9) What is 2(log(3^8)+ log3(3^4 – 7^2)) written as a single logarithm? b. log3(2z^2) Which expression is equivalent to logw (x^2 -6)^4 / 3√x^2 + 8) ? c. 4logw(x^2 -6) – 1/3 logw(x^2 + 8) Given log(3^2)= 0.631 and log(3^7)= 1.771, what is log(3^14)? c. 2.402 Which expression is equivalent to log(8^4a) (b-4)/c^4)? b. log(8^4) + log(8^4) + log(8(b-4)-4log(8^c) Which expression is equivalent to log12 (1/2 / 8w)? b. log(12^1/2) – (log12^8 + 12w) Which of the following is equivalent to log9w? a. log9 + logw Which expression is equivalent to log6(4a) (b-4/c^4)? b. log8(4) + log8(a) +(log8(b-4)-4log8c) Which of the following is equivalent to log (1/9)/k? a. log1/9 -logk The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L= 10log I/I(0), where I(0) = 10^-12 and is the least intense sound a human ear can hear. What is the approximate loudness of the dinner conversation, with a sound intensity of 10-7, Rajah has with his parents? d. 50 Db Which expression is equivalent to logc (x^2 – 1)/5x ? c. logc (x^2 – 1)-(logc5 + logcx) Given log4(3) = 0.792 and log4(21) = 2.196 what is log4(7)? a. 1.404 Which expression is equivalent to log18 – log(p + 2)? b. log 18/p+2 Which expression is equivalent to log3(x + 4)? c. log3 + log(x + 4)

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