How do you solve #2^ { 2x + 3} = 5^ { x + 1}#?

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Answer 1 · 2017-06-17T19:34:15

Given: #2^ { 2x + 3} = 5^ { x + 1}#

Use the natural logarithm on both sides:

#ln(2^ { 2x + 3}) = ln(5^ { x + 1})#

Use the property of logarithms #ln(a^c) = cln(a)# on both sides:

#(2x + 3)ln(2) = (x + 1)ln(5)#

Use the distributive property on both sides:

#2xln(2) + 3ln(2) = xln(5) + ln(5)#

Bring the constants inside as exponents:

#xln(2^2) + ln(2^3) = xln(5) + ln(5)#

Simplify:

#xln(4) + ln(8) = xln(5) + ln(5)#

#xln(4)-xln(5)=ln(5)-ln(8)#

#x(ln(4)-ln(5)) = ln(5)-ln(8)#

#x = (ln(5)-ln(8))/(ln(4)-ln(5)#