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y3=64729y^3 = \frac{64}{729}

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Full solution

Q. y3=64729y^3 = \frac{64}{729}
  1. Identify variables: Identify the base bb, the exponent yy, and the result xx in the equation y3=64729y^3 = \frac{64}{729}.b=yb = y, y=3y = 3, x=64729x = \frac{64}{729}.
  2. Rewrite in logarithmic form: Rewrite the equation in logarithmic form using the relationship by=xb^y = x to log⁡b(x)=y\log_b(x) = y. The logarithmic form is log⁡y(64729)=3\log_y(\frac{64}{729}) = 3.
  3. Check for known base: Check if the base yy is a known number or if we need to find it.\newlineIn this case, yy is not given, so we need to find the value of yy that makes y3=64729y^3 = \frac{64}{729} true.
  4. Find cube root: Find the cube root of 64729\frac{64}{729} to determine the value of yy.\newlineCube root of 6464 is 44, and cube root of 729729 is 99, so y=49y = \frac{4}{9}.
  5. Substitute back into equation: Substitute the value of yy back into the logarithmic form to complete the equation.\newlineThe logarithmic form is log⁡49(64729)=3\log_{\frac{4}{9}}\left(\frac{64}{729}\right) = 3.

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