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Popular >

simplify ln(1000e^{an+b})

Solution

simplify

ln (1000 e^{an + b})

Solution

3 ln (10) + an + b

Solution steps

ln (1000 e^{an + b})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (1000 e^{an + b}) = ln (1000) + ln (e^{an + b})

= ln (1000) + ln (e^{an + b})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{an + b}) = (an + b) ln (e)

= ln (1000) + (an + b) ln (e)

(an + b) ln (e) = an + b

= ln (1000) + an + b

ln (1000) = 3 ln (10)

= 3 ln (10) + an + b

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Frequently Asked Questions (FAQ)

What is ln(1000e^{an+b}) ?
The solution to ln(1000e^{an+b}) is 3ln(10)+an+b