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Laws of Logarithms

Instructions: Assume that all variables are positive.

1.
Expand $log (6*10)$ using the Laws of Logarithms.
1. $log 6 + log 10$
2. $log 6 - log 10$
3. $log 60$
4. $log 6 /log 10$
2.
Expand $log (7/5)^6$ using the Laws of Logarithms.
1. $log 7 + log 5$
2. $6log7 - 6log5$
3. $log 7 - log 5$
4. $6log 7 - 6log 5$
3.
Expand $log_2 (6^5* 8^4)$ using the Laws of Logarithms.
1. $5log_2 6+log_2 8^4$
2. $log_2 6^5+log_2 8^4$
3. $5log_2 6+ 4log_2 8$
4. $log_2 6^5+ 4log_2 8$
4.
Expand $log_4 (2*11*7^4)$ using the Laws of Logarithms.
1. $log_4 2- log_4 11-log_4 7^4$
2. $log_4 2+ log_4 11+4log_4 7$
3. $log_4 2- log_4 11-4log_4 7$
4. $log_4 2+ log_4 11+ log_4 7^4$
5.
Simplify the expression $log 100^x$.
1. $2$
2. $x$
3. $2x$
4. $2^x$
6.
Expand $log_14 (d^4/s^2)$ using the Laws of Logarithms.
1. $log_14 d^4 - log_14 s^2$
2. $log_14 d^4 - 2log_14 s$
3. $4log_14 d - log_14 s^2$
4. $4log_14 d - 2log_14 s$
7.
Simplify the expression. $4^(log_4 16x)$
1. $2x$
2. $16x$
3. $4^(2x)$
4. $log 16x$
8.
Expand $log_15 k^6root8(m)$ using the Laws of Logarithms.
1. $6log_15 k + log_15 m$
2. $log_15 k + 1/8log_15 m$
3. $6log_15 k + 1/8log_15 m$
4. $log_15 k + log_15 m$
9.
Condense the logarithmic expression $log_5 a + log_5 b$ using the Laws of Logarithms.
1. $log_5(a/b)$
2. $b log_5 a$
3. $log_5 (a*b)$
4. $log_a (5*b)$
10.
Express as a single logarithm. $2log(x) - 5log(y) + 3log(z)$
1. $log((x^2 z^3)/y^5)$
2. $-30log(xyz)$
3. $-log(x^2 y^5 z^3)$
4. $log((x^2 y^5)/z^3)$
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