The subtopics that fall under logarithms and surds are surds, logarithms in different bases, and finding the number of digits. The following practice questions come with detailed explanations and video solutions.
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For the following questions answer them individually
How many values of ‘p’ satisfy the following equation:
$$(\log_5 p)^2 + \log_{5p} (5/p) = 1$$?
Which of the following surds is the greatest?
Find the sum of all the values of ‘a’ that satisfy the following equation:
$$2^{\log_7 |a+9|} = \log_7 2401$$
a, b, c and d are natural numbers less than 1000 such that $$\log _a b = 7/5$$ and $$\log _c d = 4/3$$. Given that d-b=497, what is a+c?
'$$p$$' and '$$q$$' are two positive numbers such that $$p>q$$. What is the maximum value of the expression
$$p^{\sqrt{\log _p q}} - q^{\sqrt{\log _q p}} $$
Solve: $$ \log _{10} (25-x) - \log _{2} 4 = \log_{10} x - 2\log_{10} 5 $$
$$x^{1-x}=y$$ , $$y^{1-y}=z$$ and $$z^{1-z}=x$$; x, y and z are greater than 0. Find the value of xy+yz.
$$\log _a b = 2;\log _b c = 3/2$$ and $$\log _c d = 4/3$$ How many solutions are possible for a,b,c and d if they are all natural numbers less than 1000?
What is the value of $$\frac{1}{1+a^{y-x}+a^{z-x}} + \frac{1}{1+a^{x-y}+a^{z-y}} + \frac{1}{1+a^{x-z}+a^{y-z}}$$?
For which of the following range of ‘a’ the following inequality holds good:
$$\log_a 4 + \log_{a^3} 8$$ > 1?
Find the number of zeroes before the first non-zero digit to the right of the decimal point in $$1/60^{20}$$.
$$log_{10}2 = 0.3010$$, $$log_{10}3 = 0.4771$$
$$ \log _9 X + \log _{27} \sqrt{X} = (\log _{49} 11)/(\log _7 3)$$.
Find X.
If $$\log _a {147} = X$$ and $$\log _a {63} = Y$$, find the value of $$\log _a {441}$$
The number of digits in $$(2401^{35})_7 $$ is? (Subscript represents the base in which the number is written)
For every value of 'a', how many values of b satisfy the equation $$log_{b}a+ log_{ab}a^2 + log_{a^{2}b}a^{3} =0$$, when $$a>1$$ and $$a \neq b$$? (Enter -1, if the answer cannot be determined)
Solve: $$\log 325 + 3 \log 4 - \log 455$$
What is the number of digits in the number $$60^{20}$$. (log 2 =0.3010 , log 3=0.4771) ?
If $$log_z{x}=\frac{1}{3}$$ and $$log_w{y}=\frac{1}{4}$$ where x, y, z, w are distinct natural numbers such that x, y, z, w are distinct natural numbers such that x<y<z<w, what is the minimum possible value of x+y+z+w?
Simplify the surd $$\sqrt{10+\sqrt{75}} + \sqrt{10-\sqrt{75}}$$
Find the value of log 0.24242424…, given that log 2 = 0.3010, log 3 = 0.4771, log 5 = 0.6989, log 11 = 1.0413.
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