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If log_((x+1))64=3, find the value of

If log⁡(x+1)64=3 \log _{(x+1)} 64=3 , find the value of

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Quotient property of logarithmsright chevron icon

Full solution

Q. If log⁡(x+1)64=3 \log _{(x+1)} 64=3 , find the value of
  1. Understand equation: Understand the given logarithmic equation.\newlineThe equation log⁡(x+1)64=3\log_{(x+1)} 64 = 3 means that the base (x+1)(x+1) raised to the power of 33 equals 6464.
  2. Convert to exponential form: Convert the logarithmic equation to its exponential form.\newlineUsing the definition of a logarithm, we can rewrite the equation as (x+1)3=64(x+1)^3 = 64.
  3. Solve for x: Solve for x.\newlineTo find xx, we need to take the cube root of both sides of the equation. The cube root of 6464 is 44, so we have (x+1)=4(x+1) = 4.
  4. Subtract to isolate x: Subtract 11 from both sides to isolate xx.x+1=4x + 1 = 4x=4−1x = 4 - 1x=3x = 3

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