Use the change-of-base formula to write (\log_25)(\log_59) as a single log

glamrockqueen7

glamrockqueen7

Answered question

2021-10-23

Use the change-of-base formula to write (log25)(log59) as a single logarithm.

Answer & Explanation

Caren

Caren

Skilled2021-10-24Added 96 answers

Step 1
For natural logarithms the base is e. This is the most commonly used base for logarithm.
Another common base for logarithms is 10. But a logarithm can have any positive real number as its base. And using the change-of-base formula the logarithm of any base can be expressed in terms of natural logarithms.
Step 2
The given expression to be simplified is (log25)(log59). The change-of-base formula is logab=lnblna where ln represents natural logarithm. Use this formula to express given expression as a single logarithm.
(log25)(log59)=ln5ln2ln9ln5
=ln9ln2
=log29
Hence, the given expression as a single logarithm is \log_29

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