Answer :
To write the equation [tex]\(13^x = 169\)[/tex] in its equivalent logarithmic form, let's follow these steps:
1. Identify the Base, Exponent, and Result:
- Here, the base is [tex]\(13\)[/tex].
- The exponent is [tex]\(x\)[/tex].
- The result is [tex]\(169\)[/tex].
2. Understand the Logarithmic Form:
- The logarithmic form of an exponential equation [tex]\(b^y = z\)[/tex] is [tex]\(\log_b(z) = y\)[/tex].
- The base [tex]\(b\)[/tex] in the exponential form becomes the base of the logarithm.
3. Convert the Equation:
- Given: [tex]\(13^x = 169\)[/tex].
- The base is [tex]\(13\)[/tex], the result (what [tex]\(13\)[/tex] is raised to produce) is [tex]\(169\)[/tex], and the unknown exponent is [tex]\(x\)[/tex].
- This becomes: [tex]\(\log_{13}(169) = x\)[/tex].
So, the equation in its equivalent logarithmic form is [tex]\(\log_{13}(169) = x\)[/tex].
1. Identify the Base, Exponent, and Result:
- Here, the base is [tex]\(13\)[/tex].
- The exponent is [tex]\(x\)[/tex].
- The result is [tex]\(169\)[/tex].
2. Understand the Logarithmic Form:
- The logarithmic form of an exponential equation [tex]\(b^y = z\)[/tex] is [tex]\(\log_b(z) = y\)[/tex].
- The base [tex]\(b\)[/tex] in the exponential form becomes the base of the logarithm.
3. Convert the Equation:
- Given: [tex]\(13^x = 169\)[/tex].
- The base is [tex]\(13\)[/tex], the result (what [tex]\(13\)[/tex] is raised to produce) is [tex]\(169\)[/tex], and the unknown exponent is [tex]\(x\)[/tex].
- This becomes: [tex]\(\log_{13}(169) = x\)[/tex].
So, the equation in its equivalent logarithmic form is [tex]\(\log_{13}(169) = x\)[/tex].
