How do you solve ${(1.5)}^{3 x} = 7.5$ $(1.5)^(3x)=7.5$ ?

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How do you solve ${(1.5)}^{3 x} = 7.5$ $(1.5)^(3x)=7.5$ ?

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Answer 1 · 2016-03-17T17:28:38

$x \approx 1.66$ $x~~1.66$

Explanation:

$1$ $1$ . Since the left and right sides of the equation do not have the same base, start by taking the log of both sides.

${1.5}^{3 x} = 7.5$ $1.5^(3x)=7.5$

$log ({1.5}^{3 x}) = log (7.5)$ $log(1.5^(3x))=log(7.5)$

$2$ $2$ . Use the log property, ${log}_{b} (m^{n}) = n \cdot {log}_{b} (m)$ $log_color(purple)b(color(red)m^color(blue)n)=color(blue)n*log_color(purple)b(color(red)m)$ , to simplify the left side of the equation.

$(3 x) log 1.5 = log 7.5$ $(3x)log1.5=log7.5$

$3$ $3$ . Solve for $x$ $x$ .

$3 x = \frac{log 7.5}{log 1.5}$ $3x=log7.5/log1.5$

$x = \frac{log 7.5}{3 log 1.5}$ $x=log7.5/(3log1.5)$

$color(green)(|bar(ul(color(white)(a/a)x~~1.66color(white)(a/a)|)))$

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How do you solve ${(1.5)}^{3 x} = 7.5$ $(1.5)^(3x)=7.5$ ?

1 Answer

Explanation:

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How do you solve (1.5)^(3x)=7.5(1.5)3x=7.5(1.5)^(3x)=7.5?

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How do you solve ${(1.5)}^{3 x} = 7.5$ $(1.5)^(3x)=7.5$ ?