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# Logarithms Questions - All Grades

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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. $log((x^2 y^5)/z^3)$
Express as a single logarithm: $3log a - 2log b - 4logc$
1. $log (3a - 2b - 4c)$
2. $log (a^3 - b^2 - c^4)$
3. $3log a - 2log b - 4logc$
4. $log ((a^3)/(b^2c^4))$
5. none of these are correct
Evaluate. Write in simplest form. $10^(log_(10) 3)$
1. 3
2. 10
3. 1000
4. 1/3
5. none of these are correct
Solve for x: $log_(10) (x^5) = 5$
1. 10
2. 5
3. 1
4. 0
5. none of these are correct
Solve for x: $log_5⁡125=x$
1. 25
2. 3
3. $1/5$
4. 5
Write $log_5 36=x$ in exponential form.
1. $36x = 5$
2. $5^x = 36$
3. $x^5 = 36$
4. $10^x = 36$
Solve: $log_7(x)<-1$
1. $x < 1/7$
2. $x > 1/7$
3. $0 < x < 1/7$
4. No solution
Evaluate. Write in simplest form. $e^(2 ln 10)$
1. $10$
2. $100$
3. $-2$
4. $1/2$
5. none of these are correct
Solve the logarithmic equation:

$5 log(x-2)=11$
1. $x=160.5$
2. $x=158.5$
3. $x=2.2$
4. $x=0.34$
5. $x=2.34$
Solve: $log_6(x^2-6x)=log_6(-8)$
1. -4, -2
2. 4, 2
3. 4
4. No real solution
Which expression is equivalent to $log((3x^2)/y^4)$
1. 2 log 3x + 4 log y
2. 2 log 3x - 4 log y
3. log 3 + 2 log x + 4 log y
4. log 3 + 2 log x - 4 log y
What is the solution of $log_5(4x + 25) = 3$ ?
1. $-5.5$
2. $10$
3. $25$
4. $54.5$
If $log_bx=3log_bp-(2log_bt+1/2log_br)$, then the value of $x$ is
1. $p^3/(sqrt(t^2r)$
2. $p^3t^2r^(1/2$
3. $(p^3t^2)/sqrt(r$
4. $p^3/(t^2sqrtr)$
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. $log_a (5*b)$
Simplify the expression. $4^(log_4 16x)$
1. $2x$
2. $16x$
3. $4^(2x)$
4. $log 16x$