Given the exponential equation 3^x = 243, what is the logarithmic form of the equation in base 10?

Solution:

The given exponential equation is 3^x = 243

Take logarithm on both sides

log₁₀ (3^x) = log₁₀ (243) ------->(1)

We know that

log (a^b) = b × log (a)

So we get

log₁₀ (3^x) = x ×log₁₀ (3)----------->2)

Substitute (2) in (1)

Thus log₁₀ (3^x) = log₁₀ (243)

⇒ x ×log₁₀ (3) = log₁₀ (243)

x =log₁₀ (243)/ log₁₀(3)

Therefore, the logarithmic form of the equation in base 10 is x = log₁₀(243)/ log₁₀ (3).

Given the exponential equation 3^x = 243, what is the logarithmic form of the equation in base 10?

Summary:

Given the exponential equation 3^x = 243, the logarithmic form of the equation in base 10 is x =log₁₀ (243)/ log10 (3).