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# Logarithms Questions - All Grades

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$2^x=64$ is equivalent to which of the following?
1. $log_64 x=2$
2. $log_2 64=x$
3. $log_2 x=64$
4. $log_x 64=2$
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
$6^4=1296$ is equivalent to which of the following?
1. $log_6 1296=4$
2. $log_4 1296=6$
3. $log_1296 6=3$
4. $log_6 4=1296$
Solve for x. $log_(10) (x^5) = 5$
1. 10
2. 5
3. 1
4. 0
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
$4^x=256$ is equivalent to which of the following?
1. $log_256 x=4$
2. $log_4 x=256$
3. $log_256 4=x$
4. $log_4 256=x$
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. $x=2.34$
$2^3=8$ is equivalent to which of the following?
1. $log_8 2=3$
2. $log_3 8=2$
3. $log_2 8=3$
4. $log_8 3=2$
Which of the following correctly expresses the equation in logarithmic form?

$2^6=64$
1. $log_6 2=64$
2. $log_2 6=64$
3. $log_6 64=2$
4. $log_2 64=6$
Solve for x. $log_5⁡125=x$
1. 25
2. 3
3. $1/5$
4. 5
What expression is equivalent to $3log_4x + log_4y - 4log_4z?$
1. $log_4 ((3xy)/(4z))$
2. $log_4((x^3y)/z^4)$
3. $log_4x^3yz^4$
4. $log_4x^3 + y - z^4$
Which of the following is the correctly expanded version of $log(15) - log(1/100)?$
1. $log(100 - 15)$
2. $(log(500) + log(3)) - (log(10) - log(100))$
3. $(log(5) + log(3)) - (log(1) - log(100))$
4. $(log(5) + log(30)) - (log(1) - log(10))$
Write $log_5 36=x$ in exponential form.
1. $36x = 5$
2. $5^x = 36$
3. $x^5 = 36$
4. $10^x = 36$
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. $log_a (5*b)$
$log_10 0.0001=-4$
1. $10^-3=0.001$
2. $10^-4=0.0001$
3. $10x10^-3=0.01$
4. $10x10^-4=0.001$