Solve for x, to two decimal places.

Question

BlackTom AI · Accepted Answer

The problem presents the equation 200 = 4(5)^x, and we need x to two decimals.
First, isolate the exponential term by dividing both sides by 4: (5)^x = 200 / 4 = 50.
Now, to solve for x in an exponential equation, take logarithms of both sides. Using natural logs (or common logs, it doesn’t matter), we have x = log(50) / log(5).
Evaluating the ratio with common logarithms (base 10): log10(50) ≈ 1.69897 and log10(5) ≈ 0.69897. Then x ≈ 1.69897 / 0.69897 ≈ 2.43.
Alternatively, using natural logs would give the same result since log_a(b) = ln(b)/ln(a).
Therefore, x is approximately 2.43 to two decimal places. The other options do not satisfy (5)^x = 50 when evaluated: for example, 10.00 would give (5)^10 far larger than 50, 12.15 even more, and 1.87 yields a value much less than 50.

Solve for x, to two decimal places. 单项选择题

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