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Q26.
Expert-verifiedEvaluating Logarithms Evaluate the expression.
(a) ${\mathrm{log}}_{3}{3}^{7}$ (b) ${\mathrm{log}}_{4}64$ (c) ${\mathrm{log}}_{5}125$
The given exponential form is ${\mathrm{log}}_{3}{3}^{7}$.
We have to evaluate the given expression.
We’ll use the formula: ${\mathrm{log}}_{a}\left({a}^{b}\right)=b$.
We will write ${\mathrm{log}}_{3}{3}^{7}$ in form ${\mathrm{log}}_{a}\left({a}^{b}\right)$ to find a and b. Then we’ll get the answer.
Given | ${\mathrm{log}}_{a}\left({a}^{b}\right)$ form | a | b | Answer |
${\mathrm{log}}_{3}{3}^{7}$ | ${\mathrm{log}}_{3}\left({3}^{7}\right)$ | 3 | 7 | 7 |
Hence, ${\mathrm{log}}_{3}{3}^{7}$ has value role="math" $=7$.
The given exponential form is ${\mathrm{log}}_{4}64$.
We have to evaluate the given expression.
We’ll use the formula: ${\mathrm{log}}_{a}\left({a}^{b}\right)=b$.
We will write ${\mathrm{log}}_{4}64$ in form ${\mathrm{log}}_{a}\left({a}^{b}\right)$ to find a and b. Then we’ll get the answer.
Given | ${\mathrm{log}}_{a}\left({a}^{b}\right)$ form | a | b | Answer |
${\mathrm{log}}_{4}64$ | ${\mathrm{log}}_{4}\left({4}^{3}\right)$ | 4 | 3 | 3 |
Hence, ${\mathrm{log}}_{4}64$ has value $=3$.
The given exponential form is ${\mathrm{log}}_{5}125$.
We have to evaluate the given expression.
We’ll use the formula: ${\mathrm{log}}_{a}\left({a}^{b}\right)=b$.
We will write ${\mathrm{log}}_{5}125$ in form ${\mathrm{log}}_{a}\left({a}^{b}\right)$ to find a and b. Then we’ll get the answer.
Given | ${\mathrm{log}}_{a}\left({a}^{b}\right)$ form | a | b | Answer |
${\mathrm{log}}_{5}125$ | ${\mathrm{log}}_{5}\left({5}^{3}\right)$ | 5 | 3 | 3 |
Hence, ${\mathrm{log}}_{5}125$ has value $=3$.
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