If \(6^x - 6^{x-1} = 30\), then the value of \(\dfrac{2x-1}{2x+3}\) is:
\(\tfrac{3}{7}\)
\(6^x - 6^{x-1} = 30\) can be written as \(6^{x-1}(6-1) = 30\), so \(6^{x-1}\times5=30\).
This gives \(6^{x-1}=6\), so \(x-1=1\), meaning \(x=2\).
Substituting into the required expression: \(\dfrac{2x-1}{2x+3} = \dfrac{2(2)-1}{2(2)+3} = \dfrac{3}{7}\).
Hence, the value of the expression is \(\tfrac{3}{7}\).
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Important Questions from Surds and Indices
The value of \(\frac{{{{\left( {251} \right)}^3} + {{\left( {249} \right)}^3}}}{{25.1 \times 25.1 - 624.99 + 24.9 \times 24.9}}\) is 5 × 10 k , where the value of k is :
Find the value of m in \(\left(\frac{2}{7}\right)^{-3} \times \left(\frac{2}{7}\right)^{-5}=\left (\frac{2}{7}\right)^{-3m+1}\)
If √625 = 25; then√(.00000625/25)is:
A. 0.0025
B. 0.001
C. 0.0001
D. 0.0005Find the value of:
\(\sqrt{150}-\sqrt{54}-\sqrt{24}\)
If \(\sqrt{4624}=68\) , then the value of:
\(\sqrt{46.24}+\sqrt{0.4624}+\sqrt{0.004624}\)
