Use logarithms to solve the equation. Round your answer to four decimal places. $8 \left( 2.5 ^ { 2 x - 1 } \right) = 10$
A) $x = 1.2436$
B) $x = 0.6218$
C) $x = 0.25$
D) $x = - 0.6218$
E) $x = - 1.2436$

Question

Use logarithms to solve the equation. Round your answer to four decimal places.   $8 \left( 2.5 ^ { 2 x - 1 } \right) = 10$ 
A) $x = 1.2436$
B) $x = 0.6218$
C) $x = 0.25$
D) $x = - 0.6218$
E) $x = - 1.2436$

Quizplus · Accepted Answer

First, divide both sides by 8 to get $2.5^{2x-1} = 1.25$. Take the logarithm of both sides and solve for $x$: $2x - 1 = \log_{2.5}(1.25)$. Calculate the logarithm and solve for $x$ to get approximately 0.6218.

Use Logarithms to Solve the Equation 8(2.52x−1)=108 \left( 2.5 ^ { 2 x - 1 } \right) = 108(2.52x−1)=10

Use Logarithms to Solve the Equation $8 \left( 2.5 ^ { 2 x - 1 } \right) = 10$