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Standard IX

Mathematics

Logarithms

Write the fol...

Question

Write the following in logarithmic form:
(i) $8^{3} = 512$ (ii) $32^{3 / 5} = 8$ (iii) $7^{- 2} = \frac{1}{49}$ (iv) $10^{- 2} = 0.01$ .

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Solution

Write the following in logarithmic form
(i) $8^{3} = 512$
${log}_{8} (5 / 2) = 3$

(ii) $35^{3 / 5} = 8$
${log}_{32} (8) = 3 / 5$

(iii) $7^{- 2} = 1 / 49$
${log}_{7} (\frac{1}{49}) = - 2$

(iv) $10^{- 2} = 0.01$
${log}_{10} (0.01) = - 2$

(v) $E = \frac{1}{2} m v^{2}$
So $V^{2} = \frac{2 E}{m}$
${log}_{u} (\frac{2 E}{m}) = 2$

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Similar questions

Write the following in the normal form:

(i) (5 × 10) + (6 × 1); (ii) (7 × 100) + (5 × 10) + (8 × 1); (iii) (6 × 1000) + (5 × 10) + (8 × 1); (iv) (7 × 1000) + (6 × 1); (v) (1 × 1000) + (1 × 10) .

Q. Write the following in the normal form:
(i)

(5 \times 10) + (6 \times 1)

;

(ii)

(7 \times 100) + (5 \times 100) + (8 \times 1)

;

(iii)

(6 \times 1000) + (5 \times 10) + (8 \times 1)

;

(iv)

(7 \times 1000) + (6 \times 1)

;

(v)

(1 \times 1000) + (1 \times 100)

Q. Obtain the equivalent logarithmic form of the following.
(i)

2^{4} = 16

(ii)

3^{5} = 243

(iii)

10^{- 1} = 0.1

(iv)

8^{- \frac{2}{3}} = \frac{1}{4}

(v)

25^{\frac{1}{2}} = 5

(vi)

12^{- 2} = \frac{1}{144}

Q. Express the following numbers in the exponential form:
(i)

1728

(ii)

\frac{1}{512}

(iii

0.000169

Q. Write the following intervals in set-builder form:

(i) (- 3, 0) (i i) [6, 12]

(i i i) (6, 12] (i v) [- 23, 5)

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Write the following in logarithmic form:(i) 83=512 (ii) 323/5=8 (iii) 7−2=149 (iv) 10−2=0.01.

Write the following in logarithmic form (i) 83=512log8(5/2)=3(ii) 353/5=8log32(8)=3/5(iii) 7−2=1/49log7(149)=−2(iv) 10−2=0.01log10(0.01)=−2(v) E=12mv2So V2=2Emlogu(2Em)=2

Write the following in logarithmic form:
(i) $8^{3} = 512$ (ii) $32^{3 / 5} = 8$ (iii) $7^{- 2} = \frac{1}{49}$ (iv) $10^{- 2} = 0.01$ .