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Sagot :

Answer: x = log₃₇(12)

Step - by - step explanation:

1. Remove the variable from the exponent using logarithms

37^x=12

Take the common logarithm of both sides of the equation:

log₁₀(37^x)=log₁₀12)

Use the log rule:  log_a(x^y)=y*log_a(x) to move the exponent outside the logarithm:

x*log₁₀(37)=log₁₀(12)

2. Isolate the x-variable

x*log₁₀(37)=log₁₀(12)

Divide both sides of the equation log₁₀(37) by:

x = log₁₀(12) / log₁₀(37)

Use the formula  [tex]log_{b}(x)/log_{b}(a) = log_{a} (x)[/tex]

to combine the logarithms into one:

x=log₃₇(12)

Decimal form:

x=0.6881648129099501

Hope this helps!

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