Logarithmic Equations Quiz

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If $\log_{a}m = x$, then $\log_{1/a} 1m$ equals:

$-\frac{1}{x}$

$1 - x$ (correct)

$-x$

$x$

Find the value of $x$ if the base is 10 in the equation $5\log{x} - 3\log{x}^{-1} = 3\log{x} + 1 - 5\log{x}^{-1}$:

10

1

100

0 (correct)

If $\log_{a} \log_{b} \log_{c}\frac{1}{bc} = 0$, then $abc$ equals:

$0$

$-1$

$abc$

$1$ (correct)

The value of $3^4\log_b\log_a\log_c$ is:

$1$ Signup and view all the answers

Evaluate $x$ if $\log_3 (3 + x) + \log_3 (8 - x) - \log_3 (9x - 8) = 2 - \log_3 9$:

$4$ Signup and view all the answers

If $x = \log_{abc}$, $y = \log_{bca}$, $z = \log_{cab}$, then:

$xyz = 1$ Signup and view all the answers

The number log27 is:

an irrational number Signup and view all the answers

In the equation $log_{2}x + log_{4}x = 1$, the value of x is?

$8$ Signup and view all the answers

If $log_{a}x = p$ and $log_{b}x = q$, then $log_{ab}x$ equals?

$pq$ Signup and view all the answers

The number of distinct real solutions of the equation $log_{2}(3x+1) = log_{3}(2x-1)$ is?

$1$ Signup and view all the answers

If $log_{5}a = p$ and $log_{25}a = q$, then $p^2 - q^2$ is equal to?

$0$ Signup and view all the answers

If $log_{a}b = x$, then $log_{a^2}b^3$ is equal to?

$\frac{3}{2}x$ Signup and view all the answers

If $log_{a}x = p$, $log_{b}x = q$, and $log_{ab}x = r$, then $r^2 - pq$ equals?

$0$ Signup and view all the answers

What is the value of N in the given equation 16 = 16/100 = 4/25 = (2/5)^2?

120 Signup and view all the answers

In the equation (2x)ln 2 = (3y)ln 3, 3ln x = 2ln y, what is the value of x0?

1/2 Signup and view all the answers

If the sum of the first 20 terms of the series is 460, then what is the value of x?

746/21 Signup and view all the answers

What is the logarithm of to the base 2√2?

3/5 Signup and view all the answers

If log7 2 = m, then what is log49 28 equal to?

(1+2m)/2 Signup and view all the answers

What is the value of log3 4 log4 5 log5 6 log6 7 log7 8 log8 9?

(log 9/log 3)^2 Signup and view all the answers

If a^2 + 4b^2 = 12ab, then what is log(a + 2b) equal to?

(1/2) (4 log 2 + log a + log b) Signup and view all the answers

What is the value of (0.1 + 0.01 + 0.001 + ...) equal to?

-2 log20 9 Signup and view all the answers