Solve the equation in each of the following.log105 + log10(5x + 1) = log10(x + 5) + 1

log105 + log10(5x + 1) = log10(x + 5) + 1⇒ log10(5(5x + 1)) - log10(x + 5) = 1⇒ (∵ loga(M ÷ N) = (logaM) - (logaN))⇒ ⇒ 25x + 5 = 10(x + 5)⇒ 25x + 5 = 10x + 50⇒ 25x - 10x = 50 - 5 = 45⇒ 15x = 45⇒ x = 3

Q7 of 124 Page 29

Solve the equation in each of the following.
log₁₀5 + log₁₀(5x + 1) = log₁₀(x + 5) + 1

log₁₀5 + log₁₀(5x + 1) = log₁₀(x + 5) + 1

⇒ log₁₀(5(5x + 1)) - log₁₀(x + 5) = 1

⇒

(∵ log_a(M ÷ N) = (log_aM) - (log_aN))

⇒

⇒ 25x + 5 = 10(x + 5)

⇒ 25x + 5 = 10x + 50

⇒ 25x - 10x = 50 - 5 = 45

⇒ 15x = 45

⇒ x = 3

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Solve the equation in each of the following.

log₄(8log₂x) = 2

Solve the equation in each of the following.

4log₂x - log₂5 = log₂125

Solve the equation in each of the following.

log₃25 + log₃x = 3log₃5

Questions · 124

2. Scientific notations of real numbers and logarithms

1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 9 9 9 9 9 9 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 6 6 6 6 6 6 6 6 6 6 6 6 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10

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Solve the equation in each of the following.
log₁₀5 + log₁₀(5x + 1) = log₁₀(x + 5) + 1

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