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Aptitude::Logarithm

Home > Quantitative Aptitude > Logarithm > Subjective Solved Examples

Example 1 / 1

Evaluate
(i) $$\log_{2}128$$ = ?
(ii) $$\log_{3}27$$ = ?
(iii) $$\log_{7}\left(\frac{1}{343}\right)$$ = ?
(iv) $$log_{100}\left(0.0001\right)$$ = ?
(i) Let $$\log_{2}128$$ = n
so, $$2^{n}$$ = 128
Formula used: $$a^{m}$$ = x $$\Leftrightarrow$$ m = $$\log_{a}x$$
=> $$2^{n}$$ = $$2^{7}$$ or n = 7
=> $$\log_{2}128$$ = 7 Ans.

(ii) Let $$\log_{3}27$$ = n
so, $$3^{n}$$ = 27
Formula used: $$a^{m}$$ = x $$\Leftrightarrow$$ m = $$\log_{a}x$$
=> $$3^{n}$$ = $$3^{3}$$ or n = 3
=> $$\log_{3}27$$ = 3 Ans.

(iii) Let $$\log_{7}\left(\frac{1}{343}\right)$$ = n
so, $$7^{n}$$ = $$\frac{1}{343}$$
Formula used: $$a^{m}$$ = x $$\Leftrightarrow$$ m = $$\log_{a}x$$
=> $$7^{n}$$ = $$\frac{1}{7^{3}}$$
=> $$7^{n}$$ = $$7^{-3}$$or n = -3
=> $$\log_{7}\left(\frac{1}{343}\right)$$ = -3 Ans.

(iv) Let $$log_{100}\left(0.0001\right)$$ = n
so, $$100^{n}$$ = 0.0001
Formula used: $$a^{m}$$ = x $$\Leftrightarrow$$ m = $$\log_{a}x$$
=> $$100^{n}$$ = $$\frac{1}{10000}$$
=> $$100^{n}$$ = $$\frac{1}{100^{2}}$$
=> $$100^{n}$$ = $$100^{-2}$$ or n = -2
$$log_{100}\left(0.001\right)$$ = -2 Ans.
NA
NA
(i) Simplify like below:
$$\log_{2}128$$ = $$\log_{2}2^{7}$$ = $$7 \log_{2}2^{7}$$ = 7
Formula used:
$$\log_{x}x$$ = 1 AND $$\log_{x}x^m$$ = $$m \log_{x}x^m$$

(ii) Simplify like below:
$$\log_{3}27$$ = $$\log_{3}3^{3}$$ = 3
Formula used:
$$\log_{x}x$$ = 1 AND $$\log_{x}x^m$$ = $$m \log_{x}x^m$$

(iii) Simplify like below:
$$\log_{7}\left(\frac{1}{343}\right)$$ = $$\log_{7}\left(\frac{1}{7^{3}}\right)$$
= $$\log_{7}\left(7^{-3}\right)$$ = -3
Formula used:
$$\log_{x}x$$ = 1 AND $$\log_{x}x^m$$ = $$m \log_{x}x^m$$

(iv) Simplify like below:
Let $$log_{100}\left(0.0001\right)$$ = $$log_{100}\left(\frac{1}{10000}\right)$$
= $$log_{100}\left(\frac{1}{100^{2}}\right)$$ = $$log_{100}\left(100^{-2}\right)$$ = -2
Formula used:
$$\log_{x}x$$ = 1 AND $$\log_{x}x^m$$ = $$m \log_{x}x^m$$