We read your photo as:
Solve for x: log3 81 = x. Evaluate (log 500 - log 5)/log 10 using logarithm laws.
Mathematics
ScanSolve AI Answer
Answers
2 partsStep-by-step solution
9 stepsPart b· 4 steps
Solve
Convert the logarithmic equation to an exponential equation.
The definition of a logarithm states that is equivalent to .
Applying this to :Express 81 as a power of 3.
Substitute for 81 in the equation.
Equate the exponents since the bases are the same.
The solution is .
Part c2
Evaluate using logarithm laws
Apply the logarithm law for subtraction in the numerator
.
Simplify the argument of the logarithm in the numerator.
Evaluate the numerator.
Since the base of is 10 (common logarithm), asks "10 to what power equals 100?".
Evaluate the denominator.
Substitute the evaluated numerator and denominator back into the expression.
The evaluated expression is .
Was this helpful?
Try one yourself
A new problem that tests the same skill.
Still stuck on this one?
Ask a follow-up, and the answer starts from this question.
Got a different question?Ask your own question