Question
Determine the value of the unknown. \( \log _{\mathrm{b}} 7=3 \) \( \mathrm{~b}=\square \) (Type an exact answer, using radicals as needed.)
Ask by Schmidt French. in the United States
Mar 01,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( b = \sqrt[3]{7} \)
Solution
We start with the equation given by the logarithm:
log₍b₎7 = 3
This means that b raised to the power 3 equals 7:
b³ = 7
To solve for b, take the cube root of both sides:
b = ∛7
Thus, the value of the unknown b is ∛7.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
To find the value of \( b \), we can use the definition of logarithms. The equation \( \log_{b} 7 = 3 \) translates to the exponential form, which is \( b^3 = 7 \). Now, to solve for \( b \), we take the cube root of both sides: \[ b = 7^{1/3} \] Thus, the value of \( b \) is \( \sqrt[3]{7} \).
