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kingattaskus12 eNotes educator| Certified Educator

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

`ln(5.5^x) = ln(60)`

The left-hand side of the equation is equal to the exponent of the logarithm argument because the base of the logarithm equals the base of the argument.


Simplify the left-hand side of the equation.

`1.7047x=ln(60) `

Divide each term in the equation by `1.7047` .

`(1.7047x)/(1.7047) = (ln(60))/(1.7047)`

Simplify the left-hand side of the equation by canceling the common factors.

`x = (ln(60))/(1.7047)`

Simplify the equation.

`x=0.5866ln(60) `
`x~~ 2.4017`  

justaguide eNotes educator| Certified Educator

The equation `(5.5)^x = 60` has to be solved for x.

`(5.5)^x = 60`

Take the logarithm to base 10 of both the sides.

`log((5.5)^x) = log 60`

Use the property of logarithm `log a^b = b*log a`

=> `x*log 5.5 = log 60`

=> `x = (log 60)/(log 5.5)`

Substituting the values for log 60 and log 5.5 gives

`x ~~ 2.4017`

The solution of the equation is `x = (log 60)/(log 5.5) ~~ 2.4017`

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