How do you solve ${6.5}^{x} = {8.4}^{4 x - 10}$ $6.5^x = 8.4^(4x-10)$ ?

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How do you solve ${6.5}^{x} = {8.4}^{4 x - 10}$ $6.5^x = 8.4^(4x-10)$ ?

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Answer 1 · 2016-03-04T12:42:03

I found $x = 3.2$ $x=3.2$

Explanation:

Apply the natural log to both sides:
${ln (6.5)}^{x} = {ln (8.4)}^{4 x - 10}$ $ln(6.5)^(x)=ln(8.4)^(4x-10)$
Use the fact that:
${log (a)}^{x} = x log (a)$ $log(a)^x=xlog(a)$
So we get:
$x ln (6.5) = (4 x - 10) ln (8.4)$ $xln(6.5)=(4x-10)ln(8.4)$
Rearrange:
$x ln (6.5) - 4 x ln (8.4) = - 10 ln (8.4)$ $xln(6.5)-4xln(8.4)=-10ln(8.4)$
$x [ln (6.5) - 4 ln (8.4)] = - 10 ln (8.4)$ $x[ln(6.5)-4ln(8.4)]=-10ln(8.4)$
$x = \frac{- 10 ln (8.4)}{ln (6.5) - 4 ln (8.4)} = 3.2$ $x=(-10ln(8.4))/(ln(6.5)-4ln(8.4))=3.2$

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How do you solve ${6.5}^{x} = {8.4}^{4 x - 10}$ $6.5^x = 8.4^(4x-10)$ ?

1 Answer

Explanation:

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