<PRE><B>Question 1117690</B>
2.5^x = 34.1^(2x+7)
:
rewrite both sides of = using fractions
:
(5/2)^x = (341/10)^(2x+7)
:
take natural logarithms of both sides and use the identity log(a^b) = b * log(a)
:
log(5/2) * x = log(341/10) * 2x+7
:
rewrite terms on the right side of =
:
log(5/2) * x = 2 * log(341/10) * x + 7 * log(341/10)
:
subtract 2 * log(341/10) * x from both sides of = and isolate x
:
(log(5/2) - 2 * log(341/10)) * x = 7 * log(341/10)
:
now solve for x
:
x = (7 * log(341/10)) / (log(5/2) - 2 * log(341/10))
:
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x = -4.0221 
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