27. If 10 power x = 64, what is the value of 10 power x/2+1?​

27. If 10 power x = 64, what is the value of 10 power x/2+1?​

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  1. 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

    Hope it helps. Mark as brainliest if it was helpful. Thank you.

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