Find the value of (2^3x-1 + 10) ÷ 7 = 6
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Answer:
Required numeric value of x is 2.
Step-by-step explanation:
= > [ 2^( 3x - 1 ) + 10 ] ÷ 7 = 6
= > [ 2^( 3x - 1 ) + 10 ] = 6 × 7
= > 2^( 3x - 1 ) + 10 = 42
= > 2^( 3x - 1 ) = 42 - 10
= > 2^( 3x - 1 ) = 32
= > 2^( 3x - 1 ) = 2 × 2 × 2 × 2 × 2
= > 2^( 3x - 1 ) = 2^5
From the properties of indices we know that if bases are equal then the powers or exponents must be equal to each.
Thus,
= > 3x - 1 = 5
= > 3x = 5 + 1
= > 3x = 6
= > x = 6 / 3
= > x = 2
Hence the required numeric value of x is 2.
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