Write the equation log243(81)=4/5 in exponential form.
My answer is 243^4/5=81.
Evaluate 9^log9(54).
My answer is 6.
Are these correct??
Thanks
Yes for the first one
9^log 9 of 54
but base^log same base (x) = x
so I get 54 for an answer
1.25
For the first question, the correct way to write the equation log243(81) = 4/5 in exponential form is 81 = 243^(4/5).
For the second question, the correct answer is not 6. To evaluate 9^log9(54), we need to recognize that log9(54) represents the exponent to which 9 must be raised to get 54. So, log9(54) = 2. This means that 9^log9(54) is equal to 9^2, which is 81. Therefore, the correct answer is 81, not 6.
Please let me know if you have any other questions!
Yes, both of your answers are correct!
To convert the equation log243(81) = 4/5 into exponential form, you need to remember that logarithms and exponentiation are inverse operations. In this case, the base of the logarithm is 243, and the result is 81. So, when writing the equation in exponential form, the base will be 243, and the exponent will be 4/5. Therefore, 243^(4/5) = 81.
To evaluate 9^log9(54), you need to understand that the logarithm log9(54) represents the exponent to which the base 9 must be raised to obtain 54. In this case, log9(54) equals 2, since 9^2 = 81. Therefore, the expression simplifies to 9^2 = 81, and the result is 81.