Convert the following to logarithmic form: (i) 5^2 = 25 (ii) a^5 = 64 (iii) 7^x = 100 (iv) 9^0 = 1 (v) 6^1 = 6 (vi) 3^-2 = 1/9 (vii) 10^-2 = 0.01 (viii) (81)^3/4 = 27.0.01 (viii) = 27.

(i) 5 2 = 25 ⇒ log 5 25 = 2. (ii) a 5 = 64 ⇒ log a 64 = 5. (iii) 7 x = 100 ⇒ log 7 100 = x. (iv) 9 0 = 1 ⇒ log 9 1 = 0. (v) 6 1 = 6 ⇒ log 6 6 = 1. (vi) 3 -2 = ⇒ log 3 = -2. (vii) 10 -2 = 0.01 ⇒ log 10 0.01 = -2. (viii) = 27 ⇒ log 81 27 =

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Mathematics

Convert the following to logarithmic form:
(i) 5² = 25
(ii) a⁵ = 64
(iii) 7^x = 100
(iv) 9⁰ = 1
(v) 6¹ = 6
(vi) 3^-2 = $\dfrac{1}{9}$
(vii) 10^-2 = 0.01
(viii) $(81)^{\dfrac{3}{4}}$ = 27.

Logarithms

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Answer

(i) 5² = 25

⇒ log₅ 25 = 2.

(ii) a⁵ = 64

⇒ log_a 64 = 5.

(iii) 7^x = 100

⇒ log₇ 100 = x.

(iv) 9⁰ = 1

⇒ log₉ 1 = 0.

(v) 6¹ = 6

⇒ log₆ 6 = 1.

(vi) 3^-2 = $\dfrac{1}{9}$

⇒ log₃ $\dfrac{1}{9}$ = -2.

(vii) 10^-2 = 0.01

⇒ log₁₀ 0.01 = -2.

(viii) $(81)^{\dfrac{3}{4}}$ = 27

⇒ log₈₁ 27 = $\dfrac{3}{4}$

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Mathematics

Convert the following to logarithmic form:
(i) 5² = 25
(ii) a⁵ = 64
(iii) 7^x = 100
(iv) 9⁰ = 1
(v) 6¹ = 6
(vi) 3^-2 = $\dfrac{1}{9}$
(vii) 10^-2 = 0.01
(viii) $(81)^{\dfrac{3}{4}}$ = 27.

Logarithms

Answer

Related Questions

Convert the following into exponential form:
(i) log₂32 = 5
(ii) log₃81 = 4
(iii) log₃ $\dfrac{1}{3}$ = -1
(iv) log₈4 = $\dfrac{2}{3}$
(v) log₈32 = $\dfrac{5}{3}$
(vi) log₁₀ (0.001) = -3
(vii) log₂ 0.25 = -2
(viii) log_a $\Big(\dfrac{1}{a}\Big)$ = -1

By converting to exponential form, find the values of :
(i) log₂16
(ii) log₅125
(iii) log₄8
(iv) log₉27
(v) log₁₀ (0.01)
(vi) log₇ $\dfrac{1}{7}$
(vii) log_0.5 256
(viii) log₂ 0.25

Solve the following equation for x:
log₃x = 2

Solve the following equation for x:
log_x25 = 2

Mathematics

Convert the following to logarithmic form:(i) 52 = 25(ii) a5 = 64(iii) 7x = 100(iv) 90 = 1(v) 61 = 6(vi) 3-2 = 19\dfrac{1}{9}91​(vii) 10-2 = 0.01(viii) (81)34(81)^{\dfrac{3}{4}}(81)43​ = 27.

Logarithms

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Related Questions

Convert the following into exponential form:(i) log232 = 5(ii) log381 = 4(iii) log313\dfrac{1}{3}31​ = -1(iv) log84 = 23\dfrac{2}{3}32​(v) log832 = 53\dfrac{5}{3}35​(vi) log10 (0.001) = -3(vii) log2 0.25 = -2(viii) loga (1a)\Big(\dfrac{1}{a}\Big)(a1​) = -1

By converting to exponential form, find the values of :(i) log216(ii) log5125(iii) log48(iv) log927(v) log10 (0.01)(vi) log7 17\dfrac{1}{7}71​(vii) log0.5 256(viii) log2 0.25

Solve the following equation for x:log3x = 2

Solve the following equation for x:logx25 = 2

Convert the following to logarithmic form:
(i) 5² = 25
(ii) a⁵ = 64
(iii) 7^x = 100
(iv) 9⁰ = 1
(v) 6¹ = 6
(vi) 3^-2 = $\dfrac{1}{9}$
(vii) 10^-2 = 0.01
(viii) $(81)^{\dfrac{3}{4}}$ = 27.

Convert the following into exponential form:
(i) log₂32 = 5
(ii) log₃81 = 4
(iii) log₃ $\dfrac{1}{3}$ = -1
(iv) log₈4 = $\dfrac{2}{3}$
(v) log₈32 = $\dfrac{5}{3}$
(vi) log₁₀ (0.001) = -3
(vii) log₂ 0.25 = -2
(viii) log_a $\Big(\dfrac{1}{a}\Big)$ = -1

By converting to exponential form, find the values of :
(i) log₂16
(ii) log₅125
(iii) log₄8
(iv) log₉27
(v) log₁₀ (0.01)
(vi) log₇ $\dfrac{1}{7}$
(vii) log_0.5 256
(viii) log₂ 0.25

Solve the following equation for x:
log₃x = 2

Solve the following equation for x:
log_x25 = 2