( log(7) 2 + 1/log(5) 7 ) lg 7

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To simplify this expression, let's first evaluate the logarithms:

log7 2 ≈ 0.3562 (since log7 2 is the exponent to which 7 must be raised to get 2)

log5 7 ≈ 0.8271 (similarly, log5 7 is the exponent to which 5 must be raised to get 7)

Now substitute these values back into the expression:

(0.3562 + 1/0.8271) lg 7

(0.3562 + 1.2077) lg 7

1.5639 lg 7

Now calculate lg 7:

lg 7 ≈ 0.8451

Finally, substitute this value back into the expression:

1.5639 * 0.8451 ≈ 1.3236

Therefore, the simplified value of the expression is approximately 1.3236.