"^" means exponentiation. "sqrt(x)" means square root of x, which can also be written as "x^(1/2)". The symbol ~= means approximately equal.

log 5 ~= .69897 and log 7 ~= .84510.

log(a*b) = log a + log b

log(a/b) = log a - log b

log a^b = b*log a

log (sqrt(a)) = 1/2*log a.

Find the following values, rounded to the nearest five decimals.

a) log 35 =

b) log (sqrt(35)) =

c) log 7/5 =

The prime factorization of 108 is 2^2 * 3^3. Find the simplified radical form of for the following radicals, and the approximations to five significant digits.

d) sqrt(108) =

e) 108^(1/3) =

f) An earthquake registering 5.7 is recorded one morning, and in the afternoon, another quake 27 times stronger is felt. Give the Richter reading of the second stronger quake. (Nearest tenth.)

g) What is the decibel reading of a sound that is 7 times louder than a 75 decibel reading. (Nearest decibel.)

Answers in the comments.

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log 5 ~= .69897 and log 7 ~= .84510.

a) log 35 = .69897 + .84510 = 1.54407

b) log (sqrt(35)) = 1.54407/2 = 0.77204

c) log 7/5 = .84510 - .69897 = 0.14613

The prime factorization of 108 is 2^2 * 3^3. Find the simplified radical form of for the following radicals, and the approximations to five significant digits.

d) sqrt(108) = 6 * sqrt (3) ~= 10.392

e) 108^(1/3) = = 3 * (4)^ [1/3] = 4.7622

f) An earthquake registering 5.7 is recorded one morning, and in the afternoon, another quake 27 times stronger is felt. Give the Richter reading of the second stronger quake. (Nearest tenth.)

Step 1: log 27 = 1.4313...

Step 2. 1.4313.../1.5 = 0.9542, rounds to 1.0

Step 3: 5.7 + 1.0 = 6.7

g) What is the decibel reading of a sound that is 7 times louder than a 75 decibel reading. (Nearest decibel.)

Step 1: log 7 = 0.8451...

Step 2. 0.8451 bels rounds to 8 dB when multiplied by 10.

Step 3: 75 + 8 = 83 dB.

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