Find the value of each logarithmic expression. (Note: There's only one answer for the pair of logarithmic expressions indicated below.) log7 7⁵ and 5 · log7 7
Hence, the value of each logarithmic expression is both 5.
Step-by-step explanation:
To find the value of each given two logarithmic expression, we will apply the log rules.
For the first expression
[tex] \rm{log_7 \ 7^5} [/tex]
We will apply the rule Inverse Property [tex] \log_a (a^b) = b [/tex], when an exponential number where the base is same as the base of the logarithmic is equal to its exponent. Therefore, by applying the rule we get
[tex] \rm{log_7 \ 7^5 = \boxed{5}} [/tex]
For the second expression
[tex] \rm{5 \cdot log_7 \ 7} [/tex]
Here, ignore the number 5. Focus on both same number 7, when encountering problem or question like this. We apply the rule Logarith of the Base or also known as the Identity Rule [tex] \log_a (a) = 1 [/tex], when the logarithm of an argument wherein the argument is equals to the base is 1.
Answers & Comments
Answer:
Hence, the value of each logarithmic expression is both 5.
Step-by-step explanation:
To find the value of each given two logarithmic expression, we will apply the log rules.
For the first expression
We will apply the rule Inverse Property [tex] \log_a (a^b) = b [/tex], when an exponential number where the base is same as the base of the logarithmic is equal to its exponent. Therefore, by applying the rule we get
For the second expression
Here, ignore the number 5. Focus on both same number 7, when encountering problem or question like this. We apply the rule Logarith of the Base or also known as the Identity Rule [tex] \log_a (a) = 1 [/tex], when the logarithm of an argument wherein the argument is equals to the base is 1.
Hence, the value of each logarithmic expression is both 5.