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Q9 of 124 Page 29

Prove the following equations.
log₁₀1600 = 2 + 4log₁₀2

log₁₀1600 = 2 + 4log₁₀2 = 2log₁₀10 + 4log₁₀2

Let us consider the RHS:

i.e. 2 + 4log₁₀2 = 2log₁₀10 + 4log₁₀2

(∵ log_aa = 1)

= log₁₀10² + log₁₀2⁴

(∵ log_aMⁿ = nlog_aM)

= log₁₀100 + log₁₀16

= log₁₀(100×16)

(∵ log_a(M×N) = (log_aM) + (log_aN))

= log₁₀1600

Hence LHS = RHS

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7

Solve the equation in each of the following.

8

Given log_a2 = x, log_a 3 = y and log_a 5 = z. Find the value in each of the following in terms of x, y and z.

(i) log_a15 (ii) log_a8 (iii) log_a30

(iv) (v) (vi) log_a1.5

9

Prove the following equations.

log₁₀12500 = 2 + 3log₁₀5

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Prove the following equations.

log₁₀2500 = 4 - 2log₁₀2

Questions · 124

2. Scientific notations of real numbers and logarithms

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