QuestionRewrite the equation in logarithmic form. $\left(\frac{2}{5}\right)^{m}=n$ $\square$ Additional Materials

Studdy Solution

STEP 1

1. We are given an exponential equation and need to convert it into logarithmic form.
2. The base of the exponential expression is $\frac{2}{5}$ .
3. The exponent is $m$ and the result of the exponential expression is $n$ .

STEP 2

1. Identify the components of the exponential equation.
2. Rewrite the equation in logarithmic form using the identified components.

STEP 3

Identify the base, exponent, and result in the given exponential equation:
The base is $\frac{2}{5}$ , the exponent is $m$ , and the result is $n$ .

STEP 4

Rewrite the exponential equation $\left(\frac{2}{5}\right)^{m}=n$ in logarithmic form.
The logarithmic form of the equation is:
$\log_{\frac{2}{5}}(n) = m$
This expresses that $m$ is the power to which the base $\frac{2}{5}$ must be raised to obtain $n$ .

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