Question

1. solve the exponential equation. round to the nearest hundredth. $2^{x - 4}-6 = 88$ type a response

Explanation:

Step1: Isolate the exponential term

Add 6 to both sides.
$2^{x-4} = 88 + 6$
$2^{x-4} = 94$

Step2: Convert to logarithmic form

Take $\log_2$ of both sides.
$x - 4 = \log_2(94)$

Step3: Calculate $\log_2(94)$

Use change of base formula: $\log_2(94)=\frac{\ln(94)}{\ln(2)}$
$\frac{\ln(94)}{\ln(2)} \approx \frac{4.54329}{0.69315} \approx 6.5546$

Step4: Solve for x

Add 4 to the result.
$x \approx 6.5546 + 4$

Answer:

$10.55$