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Solve for a positive value of x. log_(5)(x)=4 Answer:

Solve for a positive value of x x .\newlinelog⁡5(x)=4 \log _{5}(x)=4 \newlineAnswer:

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Full solution

Q. Solve for a positive value of x x .\newlinelog⁡5(x)=4 \log _{5}(x)=4 \newlineAnswer:
  1. Understand the logarithmic equation: Understand the logarithmic equation.\newlineThe equation log⁡5(x)=4\log_{5}(x) = 4 means that 55 raised to what power equals xx. We need to find this power.
  2. Convert to exponential equation: Convert the logarithmic equation to an exponential equation.\newlineUsing the definition of a logarithm, we can rewrite the equation as 54=x5^4 = x.
  3. Calculate 545^4: Calculate the value of 545^4.\newline545^4 means 55 multiplied by itself 44 times, which is 625625.
  4. Write down the solution: Write down the solution.\newlineTherefore, x=625x = 625 is the positive value that satisfies the equation log⁡5(x)=4\log_{5}(x) = 4.

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