Question

Question #c11ad

Answer 1

see below

Explanation:

concepts applied

• `\log_a(b^c)\rArrc\log_a(b)`
• `\log_a(b)=x\leftrightarrowa^x=b`

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if referring to the log as base 10 log, `log_10x`:
`(\log_10(225))/(\log_10(25))`

then
numerator: `\log_10(15^2)\rArr2\log_10(15)`
denominator: `\log_10(5^2)\rArr2\log_10(5)`

becomes
`(2\log_10(25))/(2\log_10(5))`
the 2's cancel, which leaves you with `(\log_10(25))/(\log_10(5))`

simplify and you get your answer.

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if referring to the log as natural log, `log_ex` or `lnx`:
`(\log_e(225))/(\log_e(25))\rArr(\ln(225))/(\ln(25))`

then
numerator: `\ln(15^2)\rArr2\ln(15)`
denominator: `\ln(5^2)\rArr2\ln(5)`

becomes
`(2\ln(25))/(2\ln(5))`
the 2's cancel, which leaves you with `(\ln(25))/(\ln(5))`

simplify and you get your answer.