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# Logarithms Questions - All Grades

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Write $64 ^(1/2) = 8$ in logarithmic form.
1. $log_64 (1/2) =8$
2. $log_(1/2) 8 =64$
3. $log_64 8 = 1/2$
4. $log_(1/2) 64 =8$
Write $log_2 8 = 3$ in exponential form.
1. $2^4 = 8$
2. $2^3 = 8$
3. $2^2 = 8$
4. $2^5 = 8$
$2^3=8$ is equivalent to which of the following?
1. $log_8 2=3$
2. $log_3 8=2$
3. $log_2 8=3$
4. $log_8 3=2$
Grade 11 Logarithms CCSS: HSF-BF.B.5, HSF-LE.A.4
$2^x=64$ is equivalent to which of the following?
1. $log_64 x=2$
2. $log_2 64=x$
3. $log_2 x=64$
4. $log_x 64=2$
What is the domain of the function $f(x)=3log_2 x ?$
1. $[0,oo)$
2. $(0,oo)$
3. $(3,oo)$
4. $[2,oo)$
5. $(-oo,oo)$
Which of the following expresses the equation in correct exponential form?

$log_10 0.0001=-4$
1. $10^-3=0.001$
2. $10^-4=0.0001$
3. $10xx10^-3=0.01$
4. $10xx10^-4=0.001$
Which of the following is not a property of logarithms?
1. log(xy) = log(x) + log(y)
2. log(x/y) = log(x) - log(y)
3. log(x^y) = y log(x)
4. log(x + y) = log(x) + log(y)
$6^4=1296$ is equivalent to which of the following?
1. $log_6 1296=4$
2. $log_4 1296=6$
3. $log_1296 6=3$
4. $log_6 4=1296$
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. $log((x^2 y^5)/z^3)$
What is the first step in solving a logarithmic equation?
1. Divide both sides by the logarithmic base
2. Rewrite the logarithmic equation as an exponential equation
3. Multiply both sides by the logarithmic base
4. Simplify the logarithmic expression on both sides
What is the value of ln(e^5)?
1. 5
2. e
3. ln(5)
4. Undefined
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
$4^x=256$ 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. $x=2.34$
Expand $log (6*10)$ using the Laws of Logarithms.
1. $log 6 + log 10$
2. $log 6 - log 10$
3. $log 60$
4. $log 6 /log 10$