Question

Use properties of logarithms to find the exact value of the expression. Do not use a calculator.logv5 6 times log v6 25=

Answer 1

We need to solve the next expression using the properties of the logarithm:

`\log _56\cdot\log _625`

Use the next logarithm property on both:

`\log _ab\text{ =}(\ln b)/(\ln a)`

So:

`\frac{\ln6}{\ln\text{ 5}}\cdot(\ln 25)/(\ln 6)`

Cancel the like terms, in this case, ln 6

Then:

`\frac{\ln \text{ 25}}{\ln 5}`

Rewrite the expression ln 25, using the next property:

`\ln x^{b\text{ }}=\text{ b}\cdot\ln \text{ x}`

Then

`\ln 25\text{ = }\ln 5^2=2\ln 5`

Simplify the like terms:

`(2\ln 5)/(\ln 5)=2`

Therefore, The result is 2.