27. If 10 power x = 64, what is the value of 10 power x/2+1?
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27. If 10 power x = 64, what is the value of 10 power x/2+1?
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Answer:
The answer is 80.
Step-by-step explanation:
10ˣ = 64 ⇔ log₁₀64 = x
log₁₀8² = x ⇒ 2×log₁₀8 = x ⇒ log₁₀8 = x/2 ..1
To find 10^(x/2)+1
substitute x/2 = log₁₀8
10^( log₁₀8 + 1) = y
10^(log₁₀8 + log₁₀10) = y (note : logₓx = 1 and logₓa + logₓb = logₓab)
10^(log₁₀80) = y
log₁₀10^(log₁₀80) = log₁₀y
(log₁₀80)×(log₁₀10) = log₁₀y (note : logₓ(a^logₙb) = (logₙb) × ( logₓa) )
log₁₀80 × 1 = log₁₀y
80 = y
y = 10^((x/2)+1) = 80
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