Question

Solve each equation. Round to the nearest ten-thousandth. Check your answers. 25²x⁺¹=144

Answer 1

$25^{2x+1}=144$ => x = 0.272, by properties of logarithm.

What is Logarithm?

• The opposite of exponentiation is the logarithm.
• This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.
• A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Given: $25^{2x+1}=144$

Taking logarithm on both sides:

log ($25^{2x+1}$) = log (144)

=> (2x + 1) log (25) = log (144) (As $log_b(a)^m = m (log_b(a))$)

=> 2x + 1 = $\frac{log144}{log25}$

=> 2x + 1 = $\frac{2.158}{1.397}$

=> 2x + 1 = 1.544

=> 2x = 0.544

=> x = 0.272

Hence, $25^{2x+1}=144$ => x = 0.272, by properties of logarithm.

To learn more about logarithms, refer to the link: brainly.com/question/25710806

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