Use properties of logarithms to condense the logarithmic expression. coefficient

Question

Use properties of logarithms to condense the logarithmic expression. coefficient is 1. Where possible, evaluate expressions Write the expression as a single logarithm whose 10gx log3 y) logarithmic exprerssi 18) 25x +2=125x-10 8 each side as a power of the same base and then equating exponents. Solve the exponential equation. Express 19)ax 7l equation. Express the solution set in terms of natural logarithms. e logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer 20) log,x + log, ( -15)-2

Explanation / Answer

17)

(1/6)(log3 x +log3 y)=(1/6)(log3 xy)

=>(1/6)(log3 x +log3 y)=log3 (xy)1/6

=>(1/6)(log3 x +log3 y)=log3  x1/6y1/6

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18)

25x+2=125x-10

=>(52)x+2=(53)x-10

=>52x+4=53x-30

=>2x+4=3x-30

=>3x-2x=4+30

=>x=34

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19)

ex+7 =4

=>x+7 =ln4

=>x=-7+ ln4

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20)

domain is x>15

log4 x +log4 (x-15)=2

=>log4 x(x-15)=2

=>x(x-15)=42

=>x2-15x=16

=>x2?-15x-16=0

=>(x+1)(x-16)=0

=>x=-1, x=16

x=-1 is not in domain

so x=16 is the only solution

PLEASE RATE IF HELPFUL.PLEASE COMMENT IF YOU HAVE ANY DOUBT

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